diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json index 9027b4401..403e8b711 100644 --- a/dev/.documenter-siteinfo.json +++ b/dev/.documenter-siteinfo.json @@ -1 +1 @@ -{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-07T08:14:51","documenter_version":"1.4.1"}} \ No newline at end of file +{"documenter":{"julia_version":"1.10.3","generation_timestamp":"2024-05-07T13:05:55","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/dev/bibliography/index.html b/dev/bibliography/index.html index 310446430..bb0c4b192 100644 --- a/dev/bibliography/index.html +++ b/dev/bibliography/index.html @@ -1,2 +1,2 @@ -Bibliography · SumOfSquares
GitHub

Bibliography

+Bibliography · SumOfSquares
GitHub

Bibliography

diff --git a/dev/constraints/index.html b/dev/constraints/index.html index e6215575f..c246aac5b 100644 --- a/dev/constraints/index.html +++ b/dev/constraints/index.html @@ -70,13 +70,13 @@ (-α) + (-1)y² + (2)xy + (-1)x² + (1)y³ + (1)x³ is SOS

constrains the polynomial to be nonnegative for every real numbers x and y. However, the set of points (x, y) for which the polynomial is constrained to be nonnegative can be specified by the domain keyword:

julia> S = @set x >= 0 && y >= 0 && x + y >= 1;
 
 julia> @constraint(model, x^3 - x^2 + 2x*y -y^2 + y^3 >= α, domain = S)
-(-α) + (-1)y² + (2)xy + (-1)x² + (1)y³ + (1)x³ is SOS

See this notebook for a detailed example.

Dual of polynomial constraints

The dual of a polynomial constraint cref is a moment serie μ as defined in MultivariateMoments. The dual can be obtained with the dual function as with classical dual values in JuMP.

μ = dual(cref)

By dual of a Sum-of-Squares constraint, we may mean different things and the meaning chosen for dual function was chosen for consistency with the definition of the JuMP dual function to ensure that generic code will work as expected with Sum-of-Squares constraints. In a Sum-of-Squares constraint, a polynomial $p$ is constraint to be SOS in some domain defined by polynomial q_i. So p(x) is constrained to be equal to s(x) = s_0(x) + s_1(x) * q_1(x) + s_2(x) * q_2(x) + ... where the s_i(x) polynomials are Sum-of-Squares. The dual of the equality constraint between p(x) and s(x) is given by SumOfSquares.MultivariateMoments.moments.

μ = moments(cref)

Note that the dual and moments may give different results. For instance, the output of dual only contains the moments corresponding to monomials of p while the output of moments may give the moments of other monomials if s(x) has more monomials than p(x). Besides, if the domain contains polynomial, equalities, only the remainder of p(x) - s(x) modulo the ideal is constrained to be zero, see Corollary 2 of [CLO13]. In that case, the output moments is the dual of the constraint on the remainder so some monomials may have different moments with dual or moments.

The dual of the Sum-of-Squares constraint on s_0(x), commonly referred to as the the matrix of moments can be obtained using moment_matrix:

ν = moment_matrix(cref)

The atomic_measure function of MultivariateMoments can be used to check if there exists an atomic measure (i.e. a measure that is a sum of Dirac measures) that has the moments given in the the moment matrix ν. This can be used for instance in polynomial optimization (see this notebook) or stability analysis (see this notebook).

References

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

[CLO13] Cox, D., Little, J., & OShea, D. Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra. Springer Science & Business Media, 2013.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization. ArXiv e-prints, 2017.

API Reference

Default choice for the maxdegree keyword:

SumOfSquares.default_maxdegree — Function
default_maxdegree(monos, domain)

Return the default maxdegree to use for certifying a polynomial with monomials monos to be Sum-of-Squares over the domain domain. By default, the maximum of the maxdegree of monos and of all multipliers of the domain are used so that at least constant multipliers can be used with a Putinar certificate.

source

Special case that is second-order cone representable:

SumOfSquares.PositiveSemidefinite2x2ConeTriangle — Type
struct PositiveSemidefinite2x2ConeTriangle <: MOI.AbstractSymmetricMatrixSetTriangle end

Cone of positive semidefinite matrices of 2 rows and 2 columns.

source

Inner approximations of the PSD cone that do not require semidefinite programming:

SumOfSquares.DiagonallyDominantConeTriangle — Type
struct DiagonallyDominantConeTriangle <: MOI.AbstractSymmetricMatrixSetTriangle
+(-α) + (-1)y² + (2)xy + (-1)x² + (1)y³ + (1)x³ is SOS

See this notebook for a detailed example.

Dual of polynomial constraints

The dual of a polynomial constraint cref is a moment serie μ as defined in MultivariateMoments. The dual can be obtained with the dual function as with classical dual values in JuMP.

μ = dual(cref)

By dual of a Sum-of-Squares constraint, we may mean different things and the meaning chosen for dual function was chosen for consistency with the definition of the JuMP dual function to ensure that generic code will work as expected with Sum-of-Squares constraints. In a Sum-of-Squares constraint, a polynomial $p$ is constraint to be SOS in some domain defined by polynomial q_i. So p(x) is constrained to be equal to s(x) = s_0(x) + s_1(x) * q_1(x) + s_2(x) * q_2(x) + ... where the s_i(x) polynomials are Sum-of-Squares. The dual of the equality constraint between p(x) and s(x) is given by SumOfSquares.MultivariateMoments.moments.

μ = moments(cref)

Note that the dual and moments may give different results. For instance, the output of dual only contains the moments corresponding to monomials of p while the output of moments may give the moments of other monomials if s(x) has more monomials than p(x). Besides, if the domain contains polynomial, equalities, only the remainder of p(x) - s(x) modulo the ideal is constrained to be zero, see Corollary 2 of [CLO13]. In that case, the output moments is the dual of the constraint on the remainder so some monomials may have different moments with dual or moments.

The dual of the Sum-of-Squares constraint on s_0(x), commonly referred to as the the matrix of moments can be obtained using moment_matrix:

ν = moment_matrix(cref)

The atomic_measure function of MultivariateMoments can be used to check if there exists an atomic measure (i.e. a measure that is a sum of Dirac measures) that has the moments given in the the moment matrix ν. This can be used for instance in polynomial optimization (see this notebook) or stability analysis (see this notebook).

References

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

[CLO13] Cox, D., Little, J., & OShea, D. Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra. Springer Science & Business Media, 2013.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization. ArXiv e-prints, 2017.

API Reference

Default choice for the maxdegree keyword:

SumOfSquares.default_maxdegree — Function
default_maxdegree(monos, domain)

Return the default maxdegree to use for certifying a polynomial with monomials monos to be Sum-of-Squares over the domain domain. By default, the maximum of the maxdegree of monos and of all multipliers of the domain are used so that at least constant multipliers can be used with a Putinar certificate.

source

Special case that is second-order cone representable:

Inner approximations of the PSD cone that do not require semidefinite programming:

SumOfSquares.DiagonallyDominantConeTriangle — Type
struct DiagonallyDominantConeTriangle <: MOI.AbstractSymmetricMatrixSetTriangle
     side_dimension::Int
 end

See Definition 4 of [AM17] for a precise definition of the last two items.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source
SumOfSquares.ScaledDiagonallyDominantConeTriangle — Type
struct ScaledDiagonallyDominantConeTriangle <: MOI.AbstractSymmetricMatrixSetTriangle
     side_dimension::Int
 end

See Definition 4 of [AM17] for a precise definition of the last two items.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source

Approximations of the cone of nonnegative polynomials:

SumOfSquares.NonnegPolyInnerCone — Type
struct NonnegPolyInnerCone{MCT <: MOI.AbstractVectorSet}
-end

Inner approximation of the cone of nonnegative polynomials defined by the set of polynomials of the form

X^\top Q X

where X is a vector of monomials and Q is a symmetric matrix that belongs to the cone psd_inner.

source
SumOfSquares.SDSOSCone — Type
const SDSOSCone = NonnegPolyInnerCone{ScaledDiagonallyDominantConeTriangle}

Scaled-diagonally-dominant-sum-of-squares cone; see [Definition 2, AM17] and NonnegPolyInnerCone.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source
SumOfSquares.DSOSCone — Type
const DSOSCone = NonnegPolyInnerCone{DiagonallyDominantConeTriangle}

Diagonally-dominant-sum-of-squares cone; see [Definition 2, AM17] and NonnegPolyInnerCone.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source

Approximations of the cone of positive semidefinite polynomial matrices:

SumOfSquares.PSDMatrixInnerCone — Type
struct PSDMatrixInnerCone{MCT <: MOI.AbstractVectorSet} <: PolyJuMP.PolynomialSet
-end

Inner approximation of the cone of polynomial matrices P(x) that are positive semidefinite for any x defined by the set of $n \times n$ polynomial matrices such that the polynomial $y^\top P(x) y$ belongs to NonnegPolyInnerCone{MCT} where y is a vector of $n$ auxiliary polynomial variables.

source
SumOfSquares.SOSMatrixCone — Type
const SOSMatrixCone = PSDMatrixInnerCone{MOI.PositiveSemidefiniteConeTriangle}

Sum-of-squares matrices cone; see [Section 3.3.2, BPT12] and PSDMatrixInnerCone.

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

source

Approximations of the cone of convex polynomials:

SumOfSquares.ConvexPolyInnerCone — Type
struct ConvexPolyInnerCone{MCT} <: PolyJuMP.PolynomialSet end

Inner approximation of the set of convex polynomials defined by the set of polynomials such that their hessian belongs to to the set PSDMatrixInnerCone{MCT}()

source
SumOfSquares.SOSConvexCone — Type
const SOSConvexCone = ConvexPolyInnerCone{MOI.PositiveSemidefiniteConeTriangle}

Sum-of-squares convex polynomials cone; see [Section 3.3.3, BPT12] and ConvexPolyInnerCone.

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

source

Approximations of the cone of copositive matrices:

SumOfSquares.CopositiveInner — Type
struct CopositiveInner{S} <: PolyJuMP.PolynomialSet
+end

Inner approximation of the cone of nonnegative polynomials defined by the set of polynomials of the form

X^\top Q X

where X is a vector of monomials and Q is a symmetric matrix that belongs to the cone psd_inner.

source
SumOfSquares.SDSOSCone — Type
const SDSOSCone = NonnegPolyInnerCone{ScaledDiagonallyDominantConeTriangle}

Scaled-diagonally-dominant-sum-of-squares cone; see [Definition 2, AM17] and NonnegPolyInnerCone.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source
SumOfSquares.DSOSCone — Type
const DSOSCone = NonnegPolyInnerCone{DiagonallyDominantConeTriangle}

Diagonally-dominant-sum-of-squares cone; see [Definition 2, AM17] and NonnegPolyInnerCone.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source

Approximations of the cone of positive semidefinite polynomial matrices:

SumOfSquares.PSDMatrixInnerCone — Type
struct PSDMatrixInnerCone{MCT <: MOI.AbstractVectorSet} <: PolyJuMP.PolynomialSet
+end

Inner approximation of the cone of polynomial matrices P(x) that are positive semidefinite for any x defined by the set of $n \times n$ polynomial matrices such that the polynomial $y^\top P(x) y$ belongs to NonnegPolyInnerCone{MCT} where y is a vector of $n$ auxiliary polynomial variables.

source
SumOfSquares.SOSMatrixCone — Type
const SOSMatrixCone = PSDMatrixInnerCone{MOI.PositiveSemidefiniteConeTriangle}

Sum-of-squares matrices cone; see [Section 3.3.2, BPT12] and PSDMatrixInnerCone.

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

source

Approximations of the cone of convex polynomials:

SumOfSquares.ConvexPolyInnerCone — Type
struct ConvexPolyInnerCone{MCT} <: PolyJuMP.PolynomialSet end

Inner approximation of the set of convex polynomials defined by the set of polynomials such that their hessian belongs to to the set PSDMatrixInnerCone{MCT}()

source
SumOfSquares.SOSConvexCone — Type
const SOSConvexCone = ConvexPolyInnerCone{MOI.PositiveSemidefiniteConeTriangle}

Sum-of-squares convex polynomials cone; see [Section 3.3.3, BPT12] and ConvexPolyInnerCone.

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

source

Approximations of the cone of copositive matrices:

SumOfSquares.CopositiveInner — Type
struct CopositiveInner{S} <: PolyJuMP.PolynomialSet
     # Inner approximation of the PSD cone, i.e. typically either
     # `SOSCone`, `DSOSCone` or `SDSOSCone`,
     psd_inner::S
@@ -141,13 +141,13 @@
     Q::MT
     basis::B
 end

Gram matrix $x^\top Q x$ where Q is a symmetric matrix indexed by the vector of polynomials of the basis basis.

source
SumOfSquares.GramMatrixAttribute — Type
GramMatrixAttribute(N)
-GramMatrixAttribute()

A constraint attribute for the GramMatrix of a constraint, that is, the positive semidefinite matrix Q indexed by the monomials in the vector X such that $X^\top Q X$ is the sum-of-squares certificate of the constraint.

source
SumOfSquares.gram_operate — Function
gram_operate(::typeof(+), p::GramMatrix, q::GramMatrix)

Computes the Gram matrix equal to the sum between p and q. On the opposite, p + q gives a polynomial equal to p + q. The polynomial p + q can also be obtained by polynomial(gram_operate(+, p, q)).

source
gram_operate(/, p::GramMatrix, α)

Computes the Gram matrix equal to p / α. On the opposite, p / α gives a polynomial equal to p / α. The polynomial p / α can also be obtained by polynomial(gram_operate(/, p, α)).

source
SumOfSquares.LagrangianMultipliers — Type
LagrangianMultipliers(N)
-LagrangianMultipliers()

A constraint attribute fot the LagrangianMultipliers associated to the inequalities of the domain of a constraint. There is one multiplier per inequality and no multiplier for equalities as the equalities are handled by reducing the polynomials over the ideal they generate instead of explicitely creating multipliers.

source
SumOfSquares.SOSDecompositionAttribute — Type
struct SOSDecompositionAttribute
+GramMatrixAttribute()

A constraint attribute for the GramMatrix of a constraint, that is, the positive semidefinite matrix Q indexed by the monomials in the vector X such that $X^\top Q X$ is the sum-of-squares certificate of the constraint.

source
SumOfSquares.gram_operate — Function
gram_operate(::typeof(+), p::GramMatrix, q::GramMatrix)

Computes the Gram matrix equal to the sum between p and q. On the opposite, p + q gives a polynomial equal to p + q. The polynomial p + q can also be obtained by polynomial(gram_operate(+, p, q)).

source
gram_operate(/, p::GramMatrix, α)

Computes the Gram matrix equal to p / α. On the opposite, p / α gives a polynomial equal to p / α. The polynomial p / α can also be obtained by polynomial(gram_operate(/, p, α)).

source
SumOfSquares.LagrangianMultipliers — Type
LagrangianMultipliers(N)
+LagrangianMultipliers()

A constraint attribute fot the LagrangianMultipliers associated to the inequalities of the domain of a constraint. There is one multiplier per inequality and no multiplier for equalities as the equalities are handled by reducing the polynomials over the ideal they generate instead of explicitely creating multipliers.

source

Bridges are automatically added using the following utilities:

PolyJuMP.bridgeable — Function
bridgeable(c::JuMP.AbstractConstraint, S::Type{<:MOI.AbstractSet})

Wrap the constraint c in JuMP.BridgeableConstraints that may be needed to bridge variables constrained in S on creation.

bridgeable(c::JuMP.AbstractConstraint, F::Type{<:MOI.AbstractFunction},
+end

A constraint attribute for the SOSDecomposition of a constraint. By default, it is computed using SOSDecomposition(gram, ranktol, dec) where gram is the value of the GramMatrixAttribute.

source

Bridges are automatically added using the following utilities:

PolyJuMP.bridgeable — Function
bridgeable(c::JuMP.AbstractConstraint, S::Type{<:MOI.AbstractSet})

Wrap the constraint c in JuMP.BridgeableConstraints that may be needed to bridge variables constrained in S on creation.

bridgeable(c::JuMP.AbstractConstraint, F::Type{<:MOI.AbstractFunction},
            S::Type{<:MOI.AbstractSet})

Wrap the constraint c in JuMP.BridgeableConstraints that may be needed to bridge F-in-S constraints.

source
PolyJuMP.bridges — Function
bridges(F::Type{<:MOI.AbstractFunction}, S::Type{<:MOI.AbstractSet})

Return a list of bridges that may be needed to bridge F-in-S constraints but not the bridges that may be needed by constraints added by the bridges.

source
bridges(S::Type{<:MOI.AbstractSet})

Return a list of bridges that may be needed to bridge variables constrained in S on creation but not the bridges that may be needed by constraints added by the bridges.

source

Chordal extension:

PolyJuMP.Bridges.Objective.ToPolynomialBridge — Type
ToPolynomialBridge{T}

ToPolynomialBridge implements the following reformulations:

  • $\min \{f(x)\}$ into $\min\{p(x)\}$
  • $\max \{f(x)\}$ into $\max\{p(x)\}$

where $f(x)$ is a scalar function and $p(x)$ is a polynomial.

Source node

ToPolynomialBridge supports:

  • MOI.ObjectiveFunction{F} where F is a MOI.AbstractScalarFunction for which convert(::Type{PolyJuMP.ScalarPolynomialFunction}, ::Type{F}). That is for instance the case for MOI.VariableIndex, MOI.ScalarAffineFunction and MOI.ScalarQuadraticFunction.

Target nodes

ToPolynomialBridge creates:

  • One objective node: MOI.ObjectiveFunction{PolyJuMP.ScalarPolynomialFunction{T}}
source
PolyJuMP.Bridges.Constraint.ToPolynomialBridge — Type
ToPolynomialBridge{T,S} <: Bridges.Constraint.AbstractBridge

ToPolynomialBridge implements the following reformulations:

  • $f(x) \in S$ into $p(x) \in S$ where $f(x)$ is a scalar function and $p(x)$ is a polynomial.

Source node

ToPolynomialBridge supports:

  • F in S where F is a MOI.AbstractScalarFunction for which

convert(::Type{PolyJuMP.ScalarPolynomialFunction}, ::Type{F}). That is for instance the case for MOI.VariableIndex, MOI.ScalarAffineFunction and MOI.ScalarQuadraticFunction.

Target nodes

ToPolynomialBridge creates:

source

SAGE extension

To use the SAGE cone in place of the Sum-of-Squares cone for an inequality constraints between polynomials, use the following:

import PolyJuMP
 PolyJuMP.setpolymodule!(model, PolyJuMP.SAGE)
PolyJuMP.SAGE.Polynomials — Type
struct Polynomials{M<:Union{Nothing,Int,MP.AbstractMonomial}} <: PolyJuMP.PolynomialSet

Sums of AM/GM Exponential for polynomials.

source
PolyJuMP.SAGE.Signomials — Type
struct Signomials{M<:Union{Nothing,Int,MP.AbstractMonomial}} <: PolyJuMP.PolynomialSet

Sums of AM/GM Exponential for signomials.

source
PolyJuMP.SAGE.SignomialsBridge — Type
SignomialsBridge{T,S,P,F} <: MOI.Bridges.Constraint.AbstractBridge

We use the Signomials Representative SR equation of [MCW21].

[MCW20] Riley Murray, Venkat Chandrasekaran, Adam Wierman "Newton Polytopes and Relative Entropy Optimization" https://arxiv.org/abs/1810.01614 [MCW21] Murray, Riley, Venkat Chandrasekaran, and Adam Wierman. "Signomials and polynomial optimization via relative entropy and partial dualization." Mathematical Programming Computation 13 (2021): 257-295. https://arxiv.org/pdf/1907.00814.pdf

source
PolyJuMP.SAGE.AGEBridge — Type
AGEBridge{T,F,G,H} <: MOI.Bridges.Constraint.AbstractBridge

The nonnegativity of x ≥ 0 in

∑ ci x^αi ≥ -c0 x^α0

can be reformulated as

∑ ci exp(αi'y) ≥ -β exp(α0'y)

In any case, it is shown to be equivalent to

∃ ν ≥ 0 s.t. D(ν, exp(1)*c) ≤ β, ∑ νi αi = α0 ∑ νi [CP16, (3)]

where N(ν, λ) = ∑ νj log(νj/λj) is the relative entropy function. The constant exp(1) can also be moved out of D into

∃ ν ≥ 0 s.t. D(ν, c) - ∑ νi ≤ β, ∑ νi αi = α0 ∑ νi [MCW21, (2)]

The relative entropy cone in MOI is (u, v, w) such that D(w, v) ≥ u. Therefore, we can either encode (β, exp(1)*c, ν) [CP16, (3)] or (β + ∑ νi, c, ν) [MCW21, (2)]. In this bridge, we use the second formulation.

Note

A direct application of the Arithmetic-Geometric mean inequality gives

∃ ν ≥ 0 s.t. D(ν, exp(1)*c) ≤ -log(-β), ∑ νi αi = α0, ∑ νi = 1 [CP16, (4)]

which is not jointly convex in (ν, c, β). The key to get the convex formulation [CP16, (3)] or [MCW21, (2)] instead is to use the convex conjugacy between the exponential and the negative entropy functions [CP16, (iv)].

[CP16] Chandrasekaran, Venkat, and Parikshit Shah. "Relative entropy relaxations for signomial optimization." SIAM Journal on Optimization 26.2 (2016): 1147-1173. [MCW21] Murray, Riley, Venkat Chandrasekaran, and Adam Wierman. "Signomials and polynomial optimization via relative entropy and partial dualization." Mathematical Programming Computation 13 (2021): 257-295. https://arxiv.org/pdf/1907.00814.pdf

source

Internal functions

SumOfSquares.Certificate.Symmetry._reorder! — Function
_reorder!(F::LinearAlgebra.Schur{T}) where {T}

Given a Schur decomposition of a, reorder it so that its eigenvalues are in in increasing order.

Note that if T<:Real, F.Schur is quasi upper triangular. By (quasi), we mean that there may be nonzero entries in S[i+1,i] representing complex conjugates. In that case, the complex conjugate are permuted together. If T<:Complex, then S is triangular.

source
SumOfSquares.Certificate.Symmetry._rotate_complex — Function
_rotate_complex(A::AbstractMatrix{T}, B::AbstractMatrix{T}; tol = Base.rtoldefault(real(T))) where {T}

Given (quasi) upper triangular matrix A and B that have the eigenvalues in the same order except the complex pairs which may need to be (signed) permuted, returns an othogonal matrix P such that P' * A * P and B have matching low triangular part. The upper triangular part will be dealt with by _sign_diag.

By (quasi), we mean that if S is a Matrix{<:Real}, then there may be nonzero entries in S[i+1,i] representing complex conjugates. If S is a Matrix{<:Complex}, then S is upper triangular so there is nothing to do.

source
PolyJuMP.QCQP._subs_ensure_moi_order — Function
_subs_ensure_moi_order(p::PolyJuMP.ScalarPolynomialFunction, old, new)

Substitutes old MP.variables(p.polynomial) with new vars, while re-sorting the MOI p.variables to get them in the correct order after substitution.

source
+end

A constraint attribute for the Decomposition of a constraint.

source
PolyJuMP.SAGE.SignomialsBridge — Type
SignomialsBridge{T,S,P,F} <: MOI.Bridges.Constraint.AbstractBridge

We use the Signomials Representative SR equation of [MCW21].

[MCW20] Riley Murray, Venkat Chandrasekaran, Adam Wierman "Newton Polytopes and Relative Entropy Optimization" https://arxiv.org/abs/1810.01614 [MCW21] Murray, Riley, Venkat Chandrasekaran, and Adam Wierman. "Signomials and polynomial optimization via relative entropy and partial dualization." Mathematical Programming Computation 13 (2021): 257-295. https://arxiv.org/pdf/1907.00814.pdf

source
PolyJuMP.SAGE.AGEBridge — Type
AGEBridge{T,F,G,H} <: MOI.Bridges.Constraint.AbstractBridge

The nonnegativity of x ≥ 0 in

∑ ci x^αi ≥ -c0 x^α0

can be reformulated as

∑ ci exp(αi'y) ≥ -β exp(α0'y)

In any case, it is shown to be equivalent to

∃ ν ≥ 0 s.t. D(ν, exp(1)*c) ≤ β, ∑ νi αi = α0 ∑ νi [CP16, (3)]

where N(ν, λ) = ∑ νj log(νj/λj) is the relative entropy function. The constant exp(1) can also be moved out of D into

∃ ν ≥ 0 s.t. D(ν, c) - ∑ νi ≤ β, ∑ νi αi = α0 ∑ νi [MCW21, (2)]

The relative entropy cone in MOI is (u, v, w) such that D(w, v) ≥ u. Therefore, we can either encode (β, exp(1)*c, ν) [CP16, (3)] or (β + ∑ νi, c, ν) [MCW21, (2)]. In this bridge, we use the second formulation.

Note

A direct application of the Arithmetic-Geometric mean inequality gives

∃ ν ≥ 0 s.t. D(ν, exp(1)*c) ≤ -log(-β), ∑ νi αi = α0, ∑ νi = 1 [CP16, (4)]

which is not jointly convex in (ν, c, β). The key to get the convex formulation [CP16, (3)] or [MCW21, (2)] instead is to use the convex conjugacy between the exponential and the negative entropy functions [CP16, (iv)].

[CP16] Chandrasekaran, Venkat, and Parikshit Shah. "Relative entropy relaxations for signomial optimization." SIAM Journal on Optimization 26.2 (2016): 1147-1173. [MCW21] Murray, Riley, Venkat Chandrasekaran, and Adam Wierman. "Signomials and polynomial optimization via relative entropy and partial dualization." Mathematical Programming Computation 13 (2021): 257-295. https://arxiv.org/pdf/1907.00814.pdf

source

Internal functions

SumOfSquares.Certificate.Symmetry.orthogonal_transformation_to — Function
orthogonal_transformation_to(A, B)

Return an orthogonal transformation U such that A = U' * B * U

Given Schur decompositions A = Z_A * S_A * Z_A' B = Z_B * S_B * Z_B' Since P' * S_A * P = D' * S_B * D, we have A = Z_A * P * Z_B' * B * Z_B * P' * Z_A'

source
SumOfSquares.Certificate.Symmetry._reorder! — Function
_reorder!(F::LinearAlgebra.Schur{T}) where {T}

Given a Schur decomposition of a, reorder it so that its eigenvalues are in in increasing order.

Note that if T<:Real, F.Schur is quasi upper triangular. By (quasi), we mean that there may be nonzero entries in S[i+1,i] representing complex conjugates. In that case, the complex conjugate are permuted together. If T<:Complex, then S is triangular.

source
SumOfSquares.Certificate.Symmetry._rotate_complex — Function
_rotate_complex(A::AbstractMatrix{T}, B::AbstractMatrix{T}; tol = Base.rtoldefault(real(T))) where {T}

Given (quasi) upper triangular matrix A and B that have the eigenvalues in the same order except the complex pairs which may need to be (signed) permuted, returns an othogonal matrix P such that P' * A * P and B have matching low triangular part. The upper triangular part will be dealt with by _sign_diag.

By (quasi), we mean that if S is a Matrix{<:Real}, then there may be nonzero entries in S[i+1,i] representing complex conjugates. If S is a Matrix{<:Complex}, then S is upper triangular so there is nothing to do.

source
PolyJuMP.QCQP._subs_ensure_moi_order — Function
_subs_ensure_moi_order(p::PolyJuMP.ScalarPolynomialFunction, old, new)

Substitutes old MP.variables(p.polynomial) with new vars, while re-sorting the MOI p.variables to get them in the correct order after substitution.

source
diff --git a/dev/generated/Extension/certificate.ipynb b/dev/generated/Extension/certificate.ipynb index 6f7cddeb0..00f2d58b3 100644 --- a/dev/generated/Extension/certificate.ipynb +++ b/dev/generated/Extension/certificate.ipynb @@ -130,12 +130,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.42e-04 \n", - " 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 3.12e-04 \n", + " 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 6.09e-04 \n", + " 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 7.80e-04 \n", "------------------------------------------------------------------\n", "status: unbounded\n", - "timings: total: 3.13e-04s = setup: 5.64e-05s + solve: 2.57e-04s\n", - "\t lin-sys: 1.45e-05s, cones: 1.59e-04s, accel: 1.58e-06s\n", + "timings: total: 7.82e-04s = setup: 6.42e-05s + solve: 7.18e-04s\n", + "\t lin-sys: 1.54e-05s, cones: 5.56e-04s, accel: 5.93e-06s\n", "------------------------------------------------------------------\n", "objective = -inf\n", "------------------------------------------------------------------\n" @@ -165,7 +165,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : INFEASIBLE\n Message from the solver:\n \"unbounded\"\n\n* Candidate solution (result #1)\n Primal status : INFEASIBLE_POINT\n Dual status : INFEASIBILITY_CERTIFICATE\n Objective value : NaN\n Dual objective value : -1.00000e+00\n\n* Work counters\n Solve time (sec) : 3.13063e-04\n" + "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : INFEASIBLE\n Message from the solver:\n \"unbounded\"\n\n* Candidate solution (result #1)\n Primal status : INFEASIBLE_POINT\n Dual status : INFEASIBILITY_CERTIFICATE\n Objective value : NaN\n Dual objective value : -1.00000e+00\n\n* Work counters\n Solve time (sec) : 7.81811e-04\n" }, "metadata": {}, "execution_count": 4 @@ -265,12 +265,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 8.53e+00 5.66e-01 3.99e+01 -2.00e+01 1.00e-01 1.85e-04 \n", + " 0| 8.53e+00 5.66e-01 3.99e+01 -2.00e+01 1.00e-01 1.84e-04 \n", " 250| 1.40e-03 5.14e-05 7.85e-06 8.28e-01 1.00e-01 3.96e-03 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 3.96e-03s = setup: 8.12e-05s + solve: 3.88e-03s\n", - "\t lin-sys: 2.45e-04s, cones: 3.37e-03s, accel: 3.87e-05s\n", + "timings: total: 3.96e-03s = setup: 8.10e-05s + solve: 3.88e-03s\n", + "\t lin-sys: 2.49e-04s, cones: 3.36e-03s, accel: 3.90e-05s\n", "------------------------------------------------------------------\n", "objective = 0.828440\n", "------------------------------------------------------------------\n" @@ -279,7 +279,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 8.28436e-01\n Dual objective value : 8.28444e-01\n\n* Work counters\n Solve time (sec) : 3.96277e-03\n" + "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 8.28436e-01\n Dual objective value : 8.28444e-01\n\n* Work counters\n Solve time (sec) : 3.95843e-03\n" }, "metadata": {}, "execution_count": 6 diff --git a/dev/generated/Extension/certificate/index.html b/dev/generated/Extension/certificate/index.html index f73a9b853..30452ad1b 100644 --- a/dev/generated/Extension/certificate/index.html +++ b/dev/generated/Extension/certificate/index.html @@ -40,12 +40,12 @@ ------------------------------------------------------------------ iter | pri res | dua res | gap | obj | scale | time (s) ------------------------------------------------------------------ - 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.37e-04 - 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 3.24e-04 + 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.64e-04 + 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 3.33e-04 ------------------------------------------------------------------ status: unbounded -timings: total: 3.26e-04s = setup: 5.69e-05s + solve: 2.69e-04s - lin-sys: 1.43e-05s, cones: 1.76e-04s, accel: 1.63e-06s +timings: total: 3.35e-04s = setup: 5.62e-05s + solve: 2.78e-04s + lin-sys: 1.45e-05s, cones: 1.59e-04s, accel: 1.49e-06s ------------------------------------------------------------------ objective = -inf ------------------------------------------------------------------

We can see that the problem is infeasible, meaning that no lower bound was found.

solution_summary(model)
* Solver : Dual model with SCS attached
@@ -63,7 +63,7 @@
   Dual objective value : -1.00000e+00
 
 * Work counters
-  Solve time (sec)   : 3.25697e-04
+  Solve time (sec)   : 3.34615e-04

We now define the Schmüdgen's certificate:

import MultivariateBases as MB
 const SOS = SumOfSquares
 const SOSC = SOS.Certificate
@@ -126,5 +126,5 @@
   Dual objective value : 8.28444e-01
 
 * Work counters
-  Solve time (sec)   : 4.01555e-03
-

This page was generated using Literate.jl.

+ Solve time (sec) : 3.97054e-03 +

This page was generated using Literate.jl.

diff --git a/dev/generated/Extension/hypercube/index.html b/dev/generated/Extension/hypercube/index.html index 03a46bd3e..cf02227f9 100644 --- a/dev/generated/Extension/hypercube/index.html +++ b/dev/generated/Extension/hypercube/index.html @@ -56,4 +56,4 @@ @constraint(model, c, deno * p >= deno, domain = S) optimize!(model) @show termination_status(model) -end
min_algebraic_rational (generic function with 1 method)

With d = 0, it's the same as previously

min_algebraic_rational(H, 0)
INFEASIBLE::TerminationStatusCode = 2

But with d = 1, we can find the correct lower bound

min_algebraic_rational(H, 1)
OPTIMAL::TerminationStatusCode = 1

This page was generated using Literate.jl.

+end
min_algebraic_rational (generic function with 1 method)

With d = 0, it's the same as previously

min_algebraic_rational(H, 0)
INFEASIBLE::TerminationStatusCode = 2

But with d = 1, we can find the correct lower bound

min_algebraic_rational(H, 1)
OPTIMAL::TerminationStatusCode = 1

This page was generated using Literate.jl.

diff --git a/dev/generated/Extension/typed.ipynb b/dev/generated/Extension/typed.ipynb index d43006c15..5d4584ece 100644 --- a/dev/generated/Extension/typed.ipynb +++ b/dev/generated/Extension/typed.ipynb @@ -47,7 +47,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 5.07116e-04\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 4.58002e-04\n" }, "metadata": {}, "execution_count": 1 @@ -141,7 +141,7 @@ "name": "stdout", "output_type": "stream", "text": [ - " 292.345 μs (6275 allocations: 1.33 MiB)\n" + " 292.747 μs (6275 allocations: 1.33 MiB)\n" ] }, { @@ -178,7 +178,7 @@ "name": "stdout", "output_type": "stream", "text": [ - " 417.227 μs (8486 allocations: 1.21 MiB)\n" + " 415.225 μs (8486 allocations: 1.21 MiB)\n" ] }, { @@ -250,7 +250,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 2.41113e-03\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 2.41399e-03\n" }, "metadata": {}, "execution_count": 5 diff --git a/dev/generated/Extension/typed/index.html b/dev/generated/Extension/typed/index.html index 19403e185..babdd98d3 100644 --- a/dev/generated/Extension/typed/index.html +++ b/dev/generated/Extension/typed/index.html @@ -21,7 +21,7 @@ Dual objective value : 0.00000e+00 * Work counters - Solve time (sec) : 4.17948e-04 + Solve time (sec) : 4.20094e-04

We see that the problem is feasible. The Sum-of-Squares decomposition can be obtained as follows:

sos_decomposition(con_ref)
(-0.6797543969221541 - 0.09754507709792246*y - 0.4175950563713448*x + 2.1931518901396174*y^2 - 0.1269606244678339*x*y - 0.8025867547845221*x^2)^2 + (0.9043573827480671 - 0.6455003192597278*y + 0.2742159536999832*x - 0.10770174782358159*y^2 - 1.2293138068800717*x*y - 0.9300160939847*x^2)^2 + (-0.5739168240154698 - 1.38535050221548*y - 0.6219655378569912*x - 0.2040924100740057*y^2 - 0.15182215880489783*x*y + 0.4443832632766482*x^2)^2 + (0.5703021360913615 - 0.5184093413621602*y + 0.3436728787624473*x + 0.2555950605470665*y^2 + 0.7618441294650047*x*y - 0.02090567376761348*x^2)^2 + (0.041400837217767876 + 0.04911040272637946*y - 0.49990658891857337*x - 0.24792145939081137*y^2 + 0.2972445689917418*x*y - 0.5054184235227418*x^2)^2 + (-0.2524531788141328 - 0.06336647012459033*y + 0.253942572224051*x - 0.10018744153048117*y^2 + 0.059601795985895156*x*y - 0.19381241255811912*x^2)^2

Why is there several implementations ? Depending in the use-case, one implementation may be more appropriate than another one. TypedPolynomials is faster than DynamicPolynomials but it requires new compilation whenever the list of variables changes. This means that TypedPolynomials is not appropriate when the number of variables is dynamic or too large. However, for a small number of variables, it can be faster. When solving Sum-of-Squares programs, the time is mostly taken by the Semidefinite programming solver. The time taken by SumOfSquares/JuMP/MathOptInterface are usually negligible or it time is taken by manipulation of JuMP or MathOptInterface functions therefore using TypedPolynomials over DynamicPolynomials may not make much difference in most cases.

One case for which using TypedPolynomials might be adequate is when using domain defined by equalities (possibly also with inequalities). Indeed, in that case, SumOfSquares computes the corresponding Gröbner basis which may take a non-negligible amount of time for large systems of equalities.

To illustrate this, consider the computation of Gröbner basis for the following system from [CLO05, p. 17]. The time taken by TypedPolynomials is below:

[CLO05] Cox, A. David & Little, John & O'Shea, Donal Using Algebraic Geometry. Graduate Texts in Mathematics, 2005. https://doi.org/10.1007/b138611

using BenchmarkTools
 @btime let
     TypedPolynomials.@polyvar x y
@@ -53,5 +53,5 @@
   Dual objective value : 0.00000e+00
 
 * Work counters
-  Solve time (sec)   : 2.37894e-03
-

We obtain the following decomposition:

dec = sos_decomposition(con_ref, 1e-6)
(-5.120614652559952e-5 + 0.0010584845447259056*y + 0.000340808664933532*x + 8.157919816740142*y^2 - 32.77710962574069*x*y + 29.436684176438884*x^2)^2 + (-1.0587801055835377e-5 + 0.00010602040011976172*y + 0.0010736461776558717*x + 26.098857671706984*y^2 - 16.09375738552047*x*y - 25.152942986047297*x^2)^2 + (2.970207075143178e-5 + 0.000794789039104227*y - 0.00016584049945627324*x - 0.12253485455459644*y^2 - 0.0918840250668785*x*y - 0.06835226465828073*x^2)^2 + (-5.17371414837382e-7 - 0.03721185223726042*y + 0.049797912979844754*x - 0.00016553966856285108*y^2 - 0.00012344309755984585*x*y - 9.081294614806447e-5*x^2)^2

We can verify that it is correct as follows:

rem(dec - poly, S.I)

\[ 3.616651653303066628549364440784429086672702169380499981343746185302734375 \cdot 10^{-09} + 7.939328636338026522517119874550896058852417925850321085025102664263115294040558 \cdot 10^{-08}y + 5.937935913909069103493283574397747333233173076923076923076923076923076923076939 \cdot 10^{-08}x - 8.92394073232828134722982582616168656386435031890869140625 \cdot 10^{-06}y^{2} - 1.3343841933410004185756037031751475296914577484130859375 \cdot 10^{-05}xy - 4.9814204763931092811990453128601075150072574615478515625 \cdot 10^{-06}x^{2} - 6.626560426307529875581773618857065836588541666666666666666666666666671272623229 \cdot 10^{-08}y^{3} - 7.115966675167821146411976466576258341471354166666666666666666666666664363688385 \cdot 10^{-08}xy^{2} - 5.8665363968814893645686847634124205796979367733001708984375 \cdot 10^{-08}x^{2}y + 4.281866075381493339171776404747596153846153846153846153846153846153846153846431 \cdot 10^{-09}y^{4} \]

Note that the difference between dec and poly is larger than between the full gram matrix because dec is obtained by dropping the lowest eigenvalues with the threshold 1e-6; see sos_decomposition.

rem(gram_matrix(con_ref) - poly, S.I)

\[ 4.28217951213599115010063358120750987012570476508699357509613037109375 \cdot 10^{-09} + 2.410877415089833983113631389640975391021362529733242132724859775643865390399207 \cdot 10^{-09}y + 1.900553150755093576243290534386268028846153846153846153846153846154529075482902 \cdot 10^{-09}x + 4.282181762828296545109196813427843153476715087890625 \cdot 10^{-09}y^{2} + 1.317522480004384988205856643617153167724609375 \cdot 10^{-15}xy + 4.28216934307557028915880437125451862812042236328125 \cdot 10^{-09}x^{2} - 4.352074256530613638460636138916015625 \cdot 10^{-14}y^{3} + 6.128431095930864103138446807861328125 \cdot 10^{-14}xy^{2} + 1.8955670366693766482057981193065643310546875 \cdot 10^{-13}x^{2}y + 4.455098580645146564795420720027043269230769230769230769230769230763767396138843 \cdot 10^{-09}y^{4} \]

This page was generated using Literate.jl.

+ Solve time (sec) : 2.43115e-03 +

We obtain the following decomposition:

dec = sos_decomposition(con_ref, 1e-6)
(-5.120614652559952e-5 + 0.0010584845447259056*y + 0.000340808664933532*x + 8.157919816740142*y^2 - 32.77710962574069*x*y + 29.436684176438884*x^2)^2 + (-1.0587801055835377e-5 + 0.00010602040011976172*y + 0.0010736461776558717*x + 26.098857671706984*y^2 - 16.09375738552047*x*y - 25.152942986047297*x^2)^2 + (2.970207075143178e-5 + 0.000794789039104227*y - 0.00016584049945627324*x - 0.12253485455459644*y^2 - 0.0918840250668785*x*y - 0.06835226465828073*x^2)^2 + (-5.17371414837382e-7 - 0.03721185223726042*y + 0.049797912979844754*x - 0.00016553966856285108*y^2 - 0.00012344309755984585*x*y - 9.081294614806447e-5*x^2)^2

We can verify that it is correct as follows:

rem(dec - poly, S.I)

\[ 3.616651653303066628549364440784429086672702169380499981343746185302734375 \cdot 10^{-09} + 7.939328636338026522517119874550896058852417925850321085025102664263115294040558 \cdot 10^{-08}y + 5.937935913909069103493283574397747333233173076923076923076923076923076923076939 \cdot 10^{-08}x - 8.92394073232828134722982582616168656386435031890869140625 \cdot 10^{-06}y^{2} - 1.3343841933410004185756037031751475296914577484130859375 \cdot 10^{-05}xy - 4.9814204763931092811990453128601075150072574615478515625 \cdot 10^{-06}x^{2} - 6.626560426307529875581773618857065836588541666666666666666666666666671272623229 \cdot 10^{-08}y^{3} - 7.115966675167821146411976466576258341471354166666666666666666666666664363688385 \cdot 10^{-08}xy^{2} - 5.8665363968814893645686847634124205796979367733001708984375 \cdot 10^{-08}x^{2}y + 4.281866075381493339171776404747596153846153846153846153846153846153846153846431 \cdot 10^{-09}y^{4} \]

Note that the difference between dec and poly is larger than between the full gram matrix because dec is obtained by dropping the lowest eigenvalues with the threshold 1e-6; see sos_decomposition.

rem(gram_matrix(con_ref) - poly, S.I)

\[ 4.28217951213599115010063358120750987012570476508699357509613037109375 \cdot 10^{-09} + 2.410877415089833983113631389640975391021362529733242132724859775643865390399207 \cdot 10^{-09}y + 1.900553150755093576243290534386268028846153846153846153846153846154529075482902 \cdot 10^{-09}x + 4.282181762828296545109196813427843153476715087890625 \cdot 10^{-09}y^{2} + 1.317522480004384988205856643617153167724609375 \cdot 10^{-15}xy + 4.28216934307557028915880437125451862812042236328125 \cdot 10^{-09}x^{2} - 4.352074256530613638460636138916015625 \cdot 10^{-14}y^{3} + 6.128431095930864103138446807861328125 \cdot 10^{-14}xy^{2} + 1.8955670366693766482057981193065643310546875 \cdot 10^{-13}x^{2}y + 4.455098580645146564795420720027043269230769230769230769230769230763767396138843 \cdot 10^{-09}y^{4} \]

This page was generated using Literate.jl.

diff --git a/dev/generated/Extension/univariate_solver.ipynb b/dev/generated/Extension/univariate_solver.ipynb index 32a9e41f1..c2fc665e0 100644 --- a/dev/generated/Extension/univariate_solver.ipynb +++ b/dev/generated/Extension/univariate_solver.ipynb @@ -37,7 +37,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "Main.var\"##24862\".MyUnivariateSolver" + "text/plain": "Main.var\"##25948\".MyUnivariateSolver" }, "metadata": {}, "execution_count": 1 diff --git a/dev/generated/Extension/univariate_solver/index.html b/dev/generated/Extension/univariate_solver/index.html index 319f1a018..cc22b964e 100644 --- a/dev/generated/Extension/univariate_solver/index.html +++ b/dev/generated/Extension/univariate_solver/index.html @@ -112,4 +112,4 @@ @polyvar x p = x^4 + 4x^3 + 6x^2 + 4x + 5 dec = decompose(p, MyUnivariateSolver.Optimizer)
(-0.9999999999999989 + 2.0000000000000018*x + x^2)^2 + (-2.000000000000003 - 2.0*x)^2

We can verify as follows that it gives a correct decomposition:

polynomial(dec)

\[ 5.000000000000011 + 4.000000000000013x + 6.000000000000009x^{2} + 4.0000000000000036x^{3} + x^{4} \]

We can also use a semidefinite solver:

import CSDP
-dec = decompose(p, CSDP.Optimizer)
(-1.4271293634654956 - 2.4208468386942927*x - 0.608679682768493*x^2)^2 + (1.7193818199786142 - 0.8390365176838647*x - 0.6942919122813989*x^2)^2 + (0.08383279228081496 - 0.14597477689220884*x + 0.3840153438672542*x^2)^2

The decomposition is different, it is the sum of 3 squares. However, it is also valid:

polynomial(dec)

\[ 5.000000000000001 + 3.999999999999997x + 5.9999999999999964x^{2} + 4.000000000000001x^{3} + 1.0000000000000004x^{4} \]

This page was generated using Literate.jl.

+dec = decompose(p, CSDP.Optimizer)
(-1.4271293634654956 - 2.4208468386942927*x - 0.608679682768493*x^2)^2 + (1.7193818199786142 - 0.8390365176838647*x - 0.6942919122813989*x^2)^2 + (0.08383279228081496 - 0.14597477689220884*x + 0.3840153438672542*x^2)^2

The decomposition is different, it is the sum of 3 squares. However, it is also valid:

polynomial(dec)

\[ 5.000000000000001 + 3.999999999999997x + 5.9999999999999964x^{2} + 4.000000000000001x^{3} + 1.0000000000000004x^{4} \]

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diff --git a/dev/generated/Getting started/circle.ipynb b/dev/generated/Getting started/circle.ipynb index 63922773d..827e826d4 100644 --- a/dev/generated/Getting started/circle.ipynb +++ b/dev/generated/Getting started/circle.ipynb @@ -70,7 +70,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 2.35970e-02\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 2.32961e-02\n" }, "metadata": {}, "execution_count": 3 diff --git a/dev/generated/Getting started/circle/index.html b/dev/generated/Getting started/circle/index.html index 9352086df..a42862852 100644 --- a/dev/generated/Getting started/circle/index.html +++ b/dev/generated/Getting started/circle/index.html @@ -23,5 +23,5 @@ Dual objective value : 0.00000e+00 * Work counters - Solve time (sec) : 1.04189e-03 -

The certificate can be obtained as follows:

sos_decomposition(con_ref, 1e-6)
(1.0000000044294615*x)^2

It returns $x^2$ which is a valid certificate as: $ 1 - y^2 \equiv x^2 \pmod{x^2 + y^2 - 1} $

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+ Solve time (sec) : 9.99928e-04 +

The certificate can be obtained as follows:

sos_decomposition(con_ref, 1e-6)
(1.0000000044294615*x)^2

It returns $x^2$ which is a valid certificate as: $ 1 - y^2 \equiv x^2 \pmod{x^2 + y^2 - 1} $

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diff --git a/dev/generated/Getting started/dualization.ipynb b/dev/generated/Getting started/dualization.ipynb index 4f919e566..e3a6d6986 100644 --- a/dev/generated/Getting started/dualization.ipynb +++ b/dev/generated/Getting started/dualization.ipynb @@ -74,12 +74,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 1.30e+01 1.87e+00 2.95e+01 1.47e+01 1.00e-01 2.43e-04 \n", - " 50| 6.01e-07 2.84e-07 1.95e-06 -9.76e-07 1.00e-01 4.00e-04 \n", + " 0| 1.30e+01 1.87e+00 2.95e+01 1.47e+01 1.00e-01 2.42e-04 \n", + " 50| 6.01e-07 2.84e-07 1.95e-06 -9.76e-07 1.00e-01 3.99e-04 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 4.01e-04s = setup: 1.12e-04s + solve: 2.90e-04s\n", - "\t lin-sys: 1.85e-05s, cones: 1.72e-04s, accel: 3.27e-06s\n", + "timings: total: 4.00e-04s = setup: 1.05e-04s + solve: 2.96e-04s\n", + "\t lin-sys: 1.83e-05s, cones: 1.69e-04s, accel: 3.33e-06s\n", "------------------------------------------------------------------\n", "objective = -0.000001\n", "------------------------------------------------------------------\n" @@ -129,12 +129,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 1.97e+02 1.05e+01 4.39e+03 -2.20e+03 1.00e-01 1.24e-04 \n", - " 50| 6.29e-06 1.81e-06 2.22e-05 -1.11e-05 1.00e-01 2.72e-04 \n", + " 0| 1.97e+02 1.05e+01 4.39e+03 -2.20e+03 1.00e-01 1.22e-04 \n", + " 50| 6.29e-06 1.81e-06 2.22e-05 -1.11e-05 1.00e-01 2.70e-04 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 2.73e-04s = setup: 4.28e-05s + solve: 2.30e-04s\n", - "\t lin-sys: 1.36e-05s, cones: 1.31e-04s, accel: 2.94e-06s\n", + "timings: total: 2.71e-04s = setup: 4.10e-05s + solve: 2.30e-04s\n", + "\t lin-sys: 1.33e-05s, cones: 1.29e-04s, accel: 2.95e-06s\n", "------------------------------------------------------------------\n", "objective = -0.000011\n", "------------------------------------------------------------------\n" diff --git a/dev/generated/Getting started/dualization/index.html b/dev/generated/Getting started/dualization/index.html index 42f5f0607..0457fbd88 100644 --- a/dev/generated/Getting started/dualization/index.html +++ b/dev/generated/Getting started/dualization/index.html @@ -38,12 +38,12 @@ ------------------------------------------------------------------ iter | pri res | dua res | gap | obj | scale | time (s) ------------------------------------------------------------------ - 0| 1.30e+01 1.87e+00 2.95e+01 1.47e+01 1.00e-01 1.34e-04 - 50| 6.01e-07 2.84e-07 1.95e-06 -9.76e-07 1.00e-01 2.88e-04 + 0| 1.30e+01 1.87e+00 2.95e+01 1.47e+01 1.00e-01 1.40e-04 + 50| 6.01e-07 2.84e-07 1.95e-06 -9.76e-07 1.00e-01 2.96e-04 ------------------------------------------------------------------ status: solved -timings: total: 2.89e-04s = setup: 4.70e-05s + solve: 2.42e-04s - lin-sys: 1.68e-05s, cones: 1.30e-04s, accel: 2.83e-06s +timings: total: 2.97e-04s = setup: 4.81e-05s + solve: 2.49e-04s + lin-sys: 1.77e-05s, cones: 1.32e-04s, accel: 3.23e-06s ------------------------------------------------------------------ objective = -0.000001 ------------------------------------------------------------------

As we can see in the log, SCS reports 6 variables and 11 constraints. We can also choose to dualize the problem before it is passed to SCS as follows:

using Dualization
@@ -66,12 +66,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.97e+02  1.05e+01  4.39e+03 -2.20e+03  1.00e-01  1.39e-04
-    50| 6.29e-06  1.81e-06  2.22e-05 -1.11e-05  1.00e-01  2.88e-04
+     0| 1.97e+02  1.05e+01  4.39e+03 -2.20e+03  1.00e-01  1.33e-04
+    50| 6.29e-06  1.81e-06  2.22e-05 -1.11e-05  1.00e-01  2.81e-04
 ------------------------------------------------------------------
 status:  solved
-timings: total: 2.89e-04s = setup: 4.44e-05s + solve: 2.45e-04s
-	 lin-sys: 1.35e-05s, cones: 1.29e-04s, accel: 3.24e-06s
+timings: total: 2.81e-04s = setup: 4.38e-05s + solve: 2.38e-04s
+	 lin-sys: 1.36e-05s, cones: 1.29e-04s, accel: 2.88e-06s
 ------------------------------------------------------------------
 objective = -0.000011
 ------------------------------------------------------------------

This time, SCS reports 5 variables and 6 constraints.

Bridges operating behind the scenes

The difference comes from the fact that, when designing the JuMP interface of SCS, it was decided that the model would be read in the image form. SCS therefore declares that it only supports free variables, represented in JuMP as variables in MOI.Reals and affine semidefinite constraints, represented in JuMP as MOI.VectorAffineFunction-in-MOI.PositiveSemidefiniteConeTriangle constraints. On the other hand, SumOfSquares gave the model in kernel form so the positive semidefinite (PSD) variables were reformulated as free variables constrained to be PSD using an affine PSD constraints.

This transformation is done transparently without warning but it can be inspected using print_active_bridges. As shown below, we can see Unsupported variable: MOI.PositiveSemidefiniteConeTriangle and adding as constraint indicating that PSD variables are not supported and they are added as free variables. Then we have Unsupported constraint: MOI.VectorOfVariables-in-MOI.PositiveSemidefiniteConeTriangle indicating that SCS does not support constraining variables in the PSD cone so it will just convert it into affine expressions in the PSD cone. Of course, this is equivalent but it means that SCS will not exploit this particular structure of the problem hence solving might be less efficient.

print_active_bridges(model_scs)
 * Supported objective: MOI.ScalarAffineFunction{Float64}
@@ -154,4 +154,4 @@
   y_{\beta,\gamma} (e_\beta e_\gamma - e_{\beta_\alpha} e_{\gamma_\alpha}^\top)^\top
   & \succeq 0\\
   y_{\beta,\gamma} & \text{ free}
-\end{aligned}\]
Should I dualize or not ?
Let's study the evolution of the dimensions m and n of the semidefinite program in two extreme examples and then try to extrapolate from these.
Univariate case
Suppose p is a univariate polynomial of degree $2d$. Then n will be equal to d(d + 1)/2 for both the standard and geometric conic forms. On the other hand, m will be equal to 2d + 1 for the standard conic form and d(d + 1) / 2 - (2d + 1) for the geometric form case. So m grows linearly for the kernel form but quadratically for the image form!
Quadratic case
Suppose p is a quadratic form of d variables. Then n will be equal to d for both the standard and geometric conic forms. On the other hand, m will be equal to d(d + 1)/2 for the standard conic form and 0 for the geometric form case. So m grows quadratically for the kernel form but is zero for the image form!
In general
In general, if $s_d$ is the dimension of the space of polynomials of degree d then $m = s_{2d}$ for the kernel form and $m = s_{d}(s_{d} + 1)/2 - s_{2d}$ for the image form. As a rule of thumb, the kernel form will have a smaller m if p has a low number of variables and low degree and vice versa. Of course, you can always try with and without Dualization and see which one works best.
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+\end{aligned}\]
Should I dualize or not ?
Let's study the evolution of the dimensions m and n of the semidefinite program in two extreme examples and then try to extrapolate from these.
Univariate case
Suppose p is a univariate polynomial of degree $2d$. Then n will be equal to d(d + 1)/2 for both the standard and geometric conic forms. On the other hand, m will be equal to 2d + 1 for the standard conic form and d(d + 1) / 2 - (2d + 1) for the geometric form case. So m grows linearly for the kernel form but quadratically for the image form!
Quadratic case
Suppose p is a quadratic form of d variables. Then n will be equal to d for both the standard and geometric conic forms. On the other hand, m will be equal to d(d + 1)/2 for the standard conic form and 0 for the geometric form case. So m grows quadratically for the kernel form but is zero for the image form!
In general
In general, if $s_d$ is the dimension of the space of polynomials of degree d then $m = s_{2d}$ for the kernel form and $m = s_{d}(s_{d} + 1)/2 - s_{2d}$ for the image form. As a rule of thumb, the kernel form will have a smaller m if p has a low number of variables and low degree and vice versa. Of course, you can always try with and without Dualization and see which one works best.
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diff --git a/dev/generated/Getting started/getting_started/index.html b/dev/generated/Getting started/getting_started/index.html
index 42694881b..c51fdbcfb 100644
--- a/dev/generated/Getting started/getting_started/index.html	
+++ b/dev/generated/Getting started/getting_started/index.html	
@@ -15,4 +15,4 @@
  -2.9518518518518517      1.0                      2.0

We can get the SOS decomposition from the gram matrix as follows:

sosdec = SOSDecomposition(q)
(-2.1236350925148186*y^2 + 0.6856027338723613*x*y + 1.4043287476933908*x^2)^2 + (-0.6931517747987983*y^2 - 2.105348694339436*x*y - 0.020343251432300993*x^2)^2 + (0.09856272587979271*y^2 - 0.034050994900062574*x*y + 0.16567112157245342*x^2)^2

We now seek for the SOS decomposition of the following polynomial:

p = 4*x^4*y^6 + x^2 - x*y^2 + y^2

\[ y^{2} + x^{2} - xy^{2} + 4x^{4}y^{6} \]

We build the same model as previously with this new polynomial. Here we can use Model instead of SOSModel as we explicitly constrain p to belong to the SOS cone with p in SOSCone().

model = Model(solver)
 con_ref = @constraint(model, p in SOSCone())
 optimize!(model)
-primal_status(model)
FEASIBLE_POINT::ResultStatusCode = 1

We can query the SOS decomposition directly from the constraint reference as follows:

sos_decomposition(con_ref)
(-0.8633544111907671*y + 0.1929775871076749*x*y + 2.8118914006146728e-18*x*y^2 + 1.9748040632461146*x^2*y^3)^2 + (-1.0044005280851495e-16*y + 0.7962855107812749*x - 3.604670114761173e-17*x*y - 1.7452642425911866*x*y^2 - 5.2795306922881863e-17*x^2*y^3)^2 + (0.24383463418983628*y - 1.7639164207923265e-16*x - 1.548639212897575*x*y + 3.447822046557963e-17*x*y^2 + 0.25793362243589024*x^2*y^3)^2 + (-5.040390840687567e-17*y + 0.604920974441955*x + 4.554029379037467e-17*x*y + 0.27599821010522485*x*y^2 - 4.6874560662018034e-17*x^2*y^3)^2 + (-0.4417735074073058*y - 5.425371220674707e-17*x - 0.10009637589813167*x*y + 1.353482119225013e-17*x*y^2 - 0.18335527863613874*x^2*y^3)^2

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+primal_status(model)
FEASIBLE_POINT::ResultStatusCode = 1

We can query the SOS decomposition directly from the constraint reference as follows:

sos_decomposition(con_ref)
(-0.8633544111907671*y + 0.1929775871076749*x*y + 2.8118914006146728e-18*x*y^2 + 1.9748040632461146*x^2*y^3)^2 + (-1.0044005280851495e-16*y + 0.7962855107812749*x - 3.604670114761173e-17*x*y - 1.7452642425911866*x*y^2 - 5.2795306922881863e-17*x^2*y^3)^2 + (0.24383463418983628*y - 1.7639164207923265e-16*x - 1.548639212897575*x*y + 3.447822046557963e-17*x*y^2 + 0.25793362243589024*x^2*y^3)^2 + (-5.040390840687567e-17*y + 0.604920974441955*x + 4.554029379037467e-17*x*y + 0.27599821010522485*x*y^2 - 4.6874560662018034e-17*x^2*y^3)^2 + (-0.4417735074073058*y - 5.425371220674707e-17*x - 0.10009637589813167*x*y + 1.353482119225013e-17*x*y^2 - 0.18335527863613874*x^2*y^3)^2

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diff --git a/dev/generated/Getting started/motzkin.ipynb b/dev/generated/Getting started/motzkin.ipynb index bf20b7e78..f41a13be1 100644 --- a/dev/generated/Getting started/motzkin.ipynb +++ b/dev/generated/Getting started/motzkin.ipynb @@ -328,54 +328,54 @@ "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", " - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

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+)Example block output

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diff --git a/dev/generated/Getting started/sos_decomposition/index.html b/dev/generated/Getting started/sos_decomposition/index.html index be334b9d1..016d9a594 100644 --- a/dev/generated/Getting started/sos_decomposition/index.html +++ b/dev/generated/Getting started/sos_decomposition/index.html @@ -13,4 +13,4 @@ 1.0 0.0 … -0.6273780504812863 0.0 1.2547561009625725 0.0 4.933553565678038e-17 0.0 -0.5 - -0.6273780504812863 0.0 1.0
gram.basis.monomials' * gram.Q * gram.basis.monomials

\[ 1.0 + 9.867107131356075 \cdot 10^{-17}x + x^{2} - xy^{2} + y^{4} \]

where the matrix gram.Q is positive semidefinite, because p is SOS. If we could only get the decomposition gram.Q = V' * V, the SOS decomposition would simply be ||V * monomials||^2.

Unfortunately, we can not use Cholesky decomposition, since gram Q is only semidefinite, not definite. Hence, SumOfSquares.jl uses SVD decomposition instead and discards small singular values (in our case 1e-4).

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+ -0.6273780504812863 0.0 1.0
gram.basis.monomials' * gram.Q * gram.basis.monomials

\[ 1.0 + 9.867107131356075 \cdot 10^{-17}x + x^{2} - xy^{2} + y^{4} \]

where the matrix gram.Q is positive semidefinite, because p is SOS. If we could only get the decomposition gram.Q = V' * V, the SOS decomposition would simply be ||V * monomials||^2.

Unfortunately, we can not use Cholesky decomposition, since gram Q is only semidefinite, not definite. Hence, SumOfSquares.jl uses SVD decomposition instead and discards small singular values (in our case 1e-4).

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diff --git a/dev/generated/Getting started/sum-of-squares_matrices/index.html b/dev/generated/Getting started/sum-of-squares_matrices/index.html index 62810929e..7a08ffa69 100644 --- a/dev/generated/Getting started/sum-of-squares_matrices/index.html +++ b/dev/generated/Getting started/sum-of-squares_matrices/index.html @@ -12,9 +12,9 @@ mat_cref = @constraint(model, P in PSDCone()) optimize!(model) termination_status(model)
OPTIMAL::TerminationStatusCode = 1

While the reformulation of sos matrix to sos polynomial is rather simple, as explained in the "Sum-of-Squares reformulation" section below, there is a technical subtelty about the Newton polytope that if not handled correctly may result in an SDP of large size with bad numerical behavior. For this reason, it is recommended to model sos matrix constraints as such as will be shown in this notebook and not do the formulation manually unless there is a specific reason to do so.

As we can verify as follows, only 3 monomials are used using the sos matrix constraint.

certificate_monomials(mat_cref)
3-element DynamicPolynomials.MonomialVector{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}:
- ##48782
- x##48784
- x##48782

Sum-of-Squares reformulation

One way to obtain the reduction to an sos program is to create an intermediate vector of variable $y$ and check whether the polynomial $p(x, y) = y^\top P(x) y$ is sos. However, special care is required when approximating the Newton polytope of $p(x, y)$. Indeed, for instance if the entries of $P(x)$ are quadratic forms then the Newton polytope of $p(x, y)$ is the cartesian product between the Newton polytope of $y^\top y$ and the Newton polytope of $x^\top x$. In other words, $p(x, y)$ belongs to a family of quartic forms called biquadratic forms. This fact is important when generating the semidefinite program so that only bilinear monomials are used. So if the cheap outer approximation is used (instead of the exact polyhedral computation) for the newton polytope then it is important to use a multipartite computation approximation of the newton polytope. The multipartie exact approach may perform worse compared to the unipartite exact in certain cases though. Consider for instance the polynomial matrix $\mathrm{Diag}(x_1^1, x_2^2)$ for which $p(x, y) = x_1^2y_1^2 + x_2^2y_2^2$. For this polynomial, only the monomials $x_1y_1$ and $x_2y_2$ are needed in the SDP reformulation while the multipartite approach, as it will compute the Newton polytope as a cartesian product, will not see the dependence between $x$ and $y$ in the presence of monomials and will also select the monomials $x_1y_2$ and $x_2y_1$.

@polyvar y[1:2]
+ ##50364
+ x##50366
+ x##50364

Sum-of-Squares reformulation

One way to obtain the reduction to an sos program is to create an intermediate vector of variable $y$ and check whether the polynomial $p(x, y) = y^\top P(x) y$ is sos. However, special care is required when approximating the Newton polytope of $p(x, y)$. Indeed, for instance if the entries of $P(x)$ are quadratic forms then the Newton polytope of $p(x, y)$ is the cartesian product between the Newton polytope of $y^\top y$ and the Newton polytope of $x^\top x$. In other words, $p(x, y)$ belongs to a family of quartic forms called biquadratic forms. This fact is important when generating the semidefinite program so that only bilinear monomials are used. So if the cheap outer approximation is used (instead of the exact polyhedral computation) for the newton polytope then it is important to use a multipartite computation approximation of the newton polytope. The multipartie exact approach may perform worse compared to the unipartite exact in certain cases though. Consider for instance the polynomial matrix $\mathrm{Diag}(x_1^1, x_2^2)$ for which $p(x, y) = x_1^2y_1^2 + x_2^2y_2^2$. For this polynomial, only the monomials $x_1y_1$ and $x_2y_2$ are needed in the SDP reformulation while the multipartite approach, as it will compute the Newton polytope as a cartesian product, will not see the dependence between $x$ and $y$ in the presence of monomials and will also select the monomials $x_1y_2$ and $x_2y_1$.

@polyvar y[1:2]
 p = vec(y)' * P * vec(y)

\[ 2y_{1}^{2} + 2xy_{1}y_{2} - 2xy_{1}^{2} + x^{2}y_{2}^{2} + x^{2}y_{1}^{2} \]

We can see above that p is biquadratic polynomial in the variables x and y. Computing the Newton polytope with the cheap outer approximation without exploiting this multipartite structure gives the following 6 monomials.

X = monomials(p)
 unipartite = Certificate.NewtonDegreeBounds(tuple())
 Certificate.monomials_half_newton_polytope(X, unipartite)
6-element DynamicPolynomials.MonomialVector{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}:
@@ -34,4 +34,4 @@
  xy₁

The same reasoning can be used for monomials y[1]y[2] and x therefore whether we exploit the multipartite structure or not, we get only 3 monomials thanks to this post filter.

Certificate.monomials_half_newton_polytope(X, Certificate.NewtonFilter(unipartite))
3-element DynamicPolynomials.MonomialVector{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}:
  y₁
  xy₂
- xy₁

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+ xy₁

This page was generated using Literate.jl.

diff --git a/dev/generated/Getting started/univariate.ipynb b/dev/generated/Getting started/univariate.ipynb index 42e490ea9..7168a6164 100644 --- a/dev/generated/Getting started/univariate.ipynb +++ b/dev/generated/Getting started/univariate.ipynb @@ -124,7 +124,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : -6.00000e+00\n Dual objective value : -6.00000e+00\n\n* Work counters\n Solve time (sec) : 1.01781e-03\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : -6.00000e+00\n Dual objective value : -6.00000e+00\n\n* Work counters\n Solve time (sec) : 9.73940e-04\n" }, "metadata": {}, "execution_count": 4 @@ -349,7 +349,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : -6.00000e+00\n Dual objective value : -6.00000e+00\n\n* Work counters\n Solve time (sec) : 1.48296e-03\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : -6.00000e+00\n Dual objective value : -6.00000e+00\n\n* Work counters\n Solve time (sec) : 1.47796e-03\n" }, "metadata": {}, "execution_count": 11 diff --git a/dev/generated/Getting started/univariate/index.html b/dev/generated/Getting started/univariate/index.html index 2b3848750..144458b06 100644 --- a/dev/generated/Getting started/univariate/index.html +++ b/dev/generated/Getting started/univariate/index.html @@ -21,7 +21,7 @@ Dual objective value : -6.00000e+00 * Work counters - Solve time (sec) : 1.03807e-03 + Solve time (sec) : 1.00517e-03

We can look at the certificate that σ = -6 is a lower bound:

sos_dec = sos_decomposition(cref, 1e-4)
(-3.000000004964362 - 1.999999998797403*x + 0.9999999995176428*x^2)^2

Indeed, p + 6 = (x^2 - 2x - 3)^2 so p ≥ -6.

Extraction of minimizers

We can now find the minimizers from the moment matrix:

ν = moment_matrix(cref)
 ν.Q
3×3 SymMatrix{Float64}:
  1.0        0.0669168   3.13383
@@ -60,7 +60,7 @@
   Dual objective value : -6.00000e+00
 
 * Work counters
-  Solve time (sec)   : 1.52707e-03
+  Solve time (sec)   : 1.52016e-03

Although the gram matrix in the monomial basis:

g = gram_matrix(cref)
 @show g.basis
 g.Q
3×3 SymMatrix{Float64}:
@@ -77,4 +77,4 @@
  -0.5

We can indeed observe that we obtain the same matrix as cheby_g.Q

cheby_coefs * cheby_coefs'
3×3 Matrix{Float64}:
   6.25   5.0  -1.25
   5.0    4.0  -1.0
- -1.25  -1.0   0.25

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+ -1.25 -1.0 0.25

This page was generated using Literate.jl.

diff --git a/dev/generated/Noncommutative and Hermitian/noncommutative_variables/index.html b/dev/generated/Noncommutative and Hermitian/noncommutative_variables/index.html index 8ba91e61a..b94b49866 100644 --- a/dev/generated/Noncommutative and Hermitian/noncommutative_variables/index.html +++ b/dev/generated/Noncommutative and Hermitian/noncommutative_variables/index.html @@ -22,4 +22,4 @@ gram_matrix(con_ref).Q -sos_decomposition(con_ref, 1e-6)
(-1.0000000000000002*x - x^10*y^20*x^10)^2

This page was generated using Literate.jl.

+sos_decomposition(con_ref, 1e-6)
(-1.0000000000000002*x - x^10*y^20*x^10)^2

This page was generated using Literate.jl.

diff --git a/dev/generated/Noncommutative and Hermitian/sums_of_hermitian_squares/index.html b/dev/generated/Noncommutative and Hermitian/sums_of_hermitian_squares/index.html index dc6000823..0bec9444d 100644 --- a/dev/generated/Noncommutative and Hermitian/sums_of_hermitian_squares/index.html +++ b/dev/generated/Noncommutative and Hermitian/sums_of_hermitian_squares/index.html @@ -10,4 +10,4 @@ cone = NonnegPolyInnerCone{MOI.HermitianPositiveSemidefiniteConeTriangle}() con_ref = @constraint(model, p in cone) optimize!(model) -sos_decomposition(con_ref, 1e-6)
((-1.0000000000000002 - 0.0im)*y + (0.0 - 1.0im)*x)^2

This page was generated using Literate.jl.

+sos_decomposition(con_ref, 1e-6)
((-1.0000000000000002 - 0.0im)*y + (0.0 - 1.0im)*x)^2

This page was generated using Literate.jl.

diff --git a/dev/generated/Other Applications/bounds_in_probability/index.html b/dev/generated/Other Applications/bounds_in_probability/index.html index 37ad8d1ef..14a90e141 100644 --- a/dev/generated/Other Applications/bounds_in_probability/index.html +++ b/dev/generated/Other Applications/bounds_in_probability/index.html @@ -8,4 +8,4 @@ model = SOSModel(solver);

We create a polynomial with the monomials in monos and JuMP decision variables as coefficients as follows:

@variable(model, poly, Poly(monos))

\[ ({\_}_{1}) + ({\_}_{2})x + ({\_}_{3})x^{2} \]

Nonnegative on the support:

K = @set 0 <= x && x <= 5
 con_ref = @constraint(model, poly >= 0, domain = K)

\[ ({\_}_{1}) + ({\_}_{2})x + ({\_}_{3})x^{2} \text{ is SOS} \]

Greater than one on the event:

@constraint(model, poly >= 1, domain = (@set 4 <= x && x <= 5))

\[ ({\_}_{1} - 1) + ({\_}_{2})x + ({\_}_{3})x^{2} \text{ is SOS} \]

The bound (we use LinearAlgebra for the ⋅ syntax for the scalar product):

using LinearAlgebra
 @objective(model, Min, poly ⋅ μ)

\[ {\_}_{1} + {\_}_{2} + 1.25 {\_}_{3} \]

We verify that we found a feasible solution:

optimize!(model)
-primal_status(model)
FEASIBLE_POINT::ResultStatusCode = 1

The objective value is 1/37:

objective_value(model)
0.027027027945194515

The solution is (12x-11)^2 / 37^2:

value(poly) * 37^2

\[ 120.9999573610103 - 263.99994311062636x + 143.99998960526992x^{2} \]

This page was generated using Literate.jl.

+primal_status(model)
FEASIBLE_POINT::ResultStatusCode = 1

The objective value is 1/37:

objective_value(model)
0.027027027945194515

The solution is (12x-11)^2 / 37^2:

value(poly) * 37^2

\[ 120.9999573610103 - 263.99994311062636x + 143.99998960526992x^{2} \]

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/bilinear.ipynb b/dev/generated/Polynomial Optimization/bilinear.ipynb index b0ee923ec..62a021e86 100644 --- a/dev/generated/Polynomial Optimization/bilinear.ipynb +++ b/dev/generated/Polynomial Optimization/bilinear.ipynb @@ -172,7 +172,7 @@ " 4 -2.1000e+03 -2.1000e+03 9.66e-12 5.27e-10 9.66e-10 3.84e-08 1.93e-06 9.90e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 101ms\n", + "solve time = 94.4ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -188,7 +188,7 @@ " Dual objective value : 2.10000e+03\n", "\n", "* Work counters\n", - " Solve time (sec) : 1.00621e-01\n", + " Solve time (sec) : 9.44139e-02\n", " Barrier iterations : 4\n", "\n" ] diff --git a/dev/generated/Polynomial Optimization/bilinear/index.html b/dev/generated/Polynomial Optimization/bilinear/index.html index 8421df537..6b75d3750 100644 --- a/dev/generated/Polynomial Optimization/bilinear/index.html +++ b/dev/generated/Polynomial Optimization/bilinear/index.html @@ -84,7 +84,7 @@ 4 -2.1000e+03 -2.1000e+03 9.66e-12 5.27e-10 9.66e-10 3.84e-08 1.93e-06 9.90e-01 --------------------------------------------------------------------------------------------- Terminated with status = solved -solve time = 893μs +solve time = 926μs * Solver : Clarabel * Status @@ -100,5 +100,5 @@ Dual objective value : 2.10000e+03 * Work counters - Solve time (sec) : 8.92863e-04 - Barrier iterations : 4

This page was generated using Literate.jl.

+ Solve time (sec) : 9.26241e-04 + Barrier iterations : 4

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/bound_on_global_extremum/index.html b/dev/generated/Polynomial Optimization/bound_on_global_extremum/index.html index 71b5df037..b15ae4ae9 100644 --- a/dev/generated/Polynomial Optimization/bound_on_global_extremum/index.html +++ b/dev/generated/Polynomial Optimization/bound_on_global_extremum/index.html @@ -10,4 +10,4 @@ model = SOSModel(solver);

We create the decision variable $\gamma$ that will be the lower bound to the Goldstein-Price function. We maximize it to have the highest possible lower bound.

@variable(model, γ)
 @objective(model, Max, γ)

\[ γ \]

We constrain $\gamma$ to be a lower bound with the following constraint that ensures that $f(x_1, x_2) \ge \gamma$ for all $x_1, x_2$.

@constraint(model, f >= γ)
 
-JuMP.optimize!(model)

We verify that the solver has found a feasible solution:

JuMP.primal_status(model)
NEARLY_FEASIBLE_POINT::ResultStatusCode = 2

We can now obtain the lower bound either with value(γ) or objective_value(model):

objective_value(model)
2.999986072324649

This page was generated using Literate.jl.

+JuMP.optimize!(model)

We verify that the solver has found a feasible solution:

JuMP.primal_status(model)
NEARLY_FEASIBLE_POINT::ResultStatusCode = 2

We can now obtain the lower bound either with value(γ) or objective_value(model):

objective_value(model)
2.999986072324649

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/ellipsoid.ipynb b/dev/generated/Polynomial Optimization/ellipsoid.ipynb index 42fd90ec2..2488e2df2 100644 --- a/dev/generated/Polynomial Optimization/ellipsoid.ipynb +++ b/dev/generated/Polynomial Optimization/ellipsoid.ipynb @@ -171,7 +171,7 @@ " 6 6.0000e+00 6.0000e+00 3.18e-11 2.67e-10 9.32e-11 6.56e-10 1.82e-09 9.90e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 2.44ms\n", + "solve time = 21.5ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -187,7 +187,7 @@ " Dual objective value : -6.00000e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 2.43738e-03\n", + " Solve time (sec) : 2.15115e-02\n", " Barrier iterations : 6\n", "\n" ] @@ -256,7 +256,7 @@ " 10 5.6923e+00 5.6923e+00 2.66e-10 3.80e-10 1.21e-10 2.33e-09 1.25e-09 9.78e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 57.6ms\n", + "solve time = 59.3ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -272,7 +272,7 @@ " Dual objective value : -5.69231e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 5.76259e-02\n", + " Solve time (sec) : 5.92918e-02\n", " Barrier iterations : 10\n", "\n" ] @@ -347,7 +347,7 @@ " 17 4.0685e+00 4.0685e+00 6.90e-09 5.14e-10 6.73e-11 3.12e-08 6.67e-10 9.80e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 52.7ms\n", + "solve time = 65.6ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -363,7 +363,7 @@ " Dual objective value : -4.06848e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 5.26750e-02\n", + " Solve time (sec) : 6.55548e-02\n", " Barrier iterations : 17\n", "\n" ] @@ -439,7 +439,7 @@ " 18 4.0000e+00 4.0000e+00 2.70e-09 3.35e-10 3.91e-11 1.26e-08 4.19e-10 8.51e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 851ms\n", + "solve time = 915ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -455,7 +455,7 @@ " Dual objective value : -4.00000e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 8.51368e-01\n", + " Solve time (sec) : 9.14701e-01\n", " Barrier iterations : 18\n", "\n" ] diff --git a/dev/generated/Polynomial Optimization/ellipsoid/index.html b/dev/generated/Polynomial Optimization/ellipsoid/index.html index ccc41a4fa..21fedaf25 100644 --- a/dev/generated/Polynomial Optimization/ellipsoid/index.html +++ b/dev/generated/Polynomial Optimization/ellipsoid/index.html @@ -69,7 +69,7 @@ 6 6.0000e+00 6.0000e+00 3.18e-11 2.67e-10 9.32e-11 6.56e-10 1.82e-09 9.90e-01 --------------------------------------------------------------------------------------------- Terminated with status = solved -solve time = 30.6ms +solve time = 1.03ms * Solver : Clarabel * Status @@ -85,7 +85,7 @@ Dual objective value : -6.00000e+00 * Work counters - Solve time (sec) : 3.05659e-02 + Solve time (sec) : 1.03340e-03 Barrier iterations : 6

The second level improves the lower bound

model4 = solve(4)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -128,7 +128,7 @@
  10   5.6923e+00   5.6923e+00  2.66e-10  3.80e-10  1.21e-10  2.33e-09  1.25e-09  9.78e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 5.01ms
+solve time = 5.11ms
 * Solver : Clarabel
 
 * Status
@@ -144,7 +144,7 @@
   Dual objective value : -5.69231e+00
 
 * Work counters
-  Solve time (sec)   : 5.01134e-03
+  Solve time (sec)   : 5.10834e-03
   Barrier iterations : 10

The third level improves it even further

model6 = solve(6)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -193,7 +193,7 @@
  17   4.0685e+00   4.0685e+00  6.90e-09  5.14e-10  6.73e-11  3.12e-08  6.67e-10  9.80e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 45.6ms
+solve time = 45.8ms
 * Solver : Clarabel
 
 * Status
@@ -209,7 +209,7 @@
   Dual objective value : -4.06848e+00
 
 * Work counters
-  Solve time (sec)   : 4.55922e-02
+  Solve time (sec)   : 4.58475e-02
   Barrier iterations : 17

The fourth level finds the optimal objective value as lower bound.

model8 = solve(8)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -259,7 +259,7 @@
  18   4.0000e+00   4.0000e+00  2.70e-09  3.35e-10  3.91e-11  1.26e-08  4.19e-10  8.51e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time =  815ms
+solve time =  812ms
 * Solver : Clarabel
 
 * Status
@@ -275,5 +275,5 @@
   Dual objective value : -4.00000e+00
 
 * Work counters
-  Solve time (sec)   : 8.15305e-01
-  Barrier iterations : 18

This page was generated using Literate.jl.

+ Solve time (sec) : 8.11624e-01 + Barrier iterations : 18

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/goldstein_price.ipynb b/dev/generated/Polynomial Optimization/goldstein_price.ipynb index ff5d9103c..a88b9dab6 100644 --- a/dev/generated/Polynomial Optimization/goldstein_price.ipynb +++ b/dev/generated/Polynomial Optimization/goldstein_price.ipynb @@ -202,7 +202,7 @@ " 18 3.0000e+00 3.0001e+00 4.04e-06 3.90e-08 8.72e-10 1.21e-05 2.71e-05 0.00e+00 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved (reduced accuracy)\n", - "solve time = 50.3ms\n" + "solve time = 32.7ms\n" ] } ], @@ -227,7 +227,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Dual model with Clarabel attached\n\n* Status\n Result count : 1\n Termination status : ALMOST_OPTIMAL\n Message from the solver:\n \"ALMOST_SOLVED\"\n\n* Candidate solution (result #1)\n Primal status : NEARLY_FEASIBLE_POINT\n Dual status : NEARLY_FEASIBLE_POINT\n Objective value : 3.00006e+00\n Dual objective value : 3.00005e+00\n\n* Work counters\n Solve time (sec) : 5.03126e-02\n Barrier iterations : 18\n" + "text/plain": "* Solver : Dual model with Clarabel attached\n\n* Status\n Result count : 1\n Termination status : ALMOST_OPTIMAL\n Message from the solver:\n \"ALMOST_SOLVED\"\n\n* Candidate solution (result #1)\n Primal status : NEARLY_FEASIBLE_POINT\n Dual status : NEARLY_FEASIBLE_POINT\n Objective value : 3.00006e+00\n Dual objective value : 3.00005e+00\n\n* Work counters\n Solve time (sec) : 3.26569e-02\n Barrier iterations : 18\n" }, "metadata": {}, "execution_count": 7 diff --git a/dev/generated/Polynomial Optimization/goldstein_price/index.html b/dev/generated/Polynomial Optimization/goldstein_price/index.html index d981de38d..757e86423 100644 --- a/dev/generated/Polynomial Optimization/goldstein_price/index.html +++ b/dev/generated/Polynomial Optimization/goldstein_price/index.html @@ -62,7 +62,7 @@ 18 3.0000e+00 3.0001e+00 4.04e-06 3.90e-08 8.72e-10 1.21e-05 2.71e-05 0.00e+00 --------------------------------------------------------------------------------------------- Terminated with status = solved (reduced accuracy) -solve time = 22.8ms

The lower bound found is 3

solution_summary(model)
* Solver : Dual model with Clarabel attached
+solve time = 17.5ms

The lower bound found is 3

solution_summary(model)
* Solver : Dual model with Clarabel attached
 
 * Status
   Result count       : 1
@@ -77,7 +77,7 @@
   Dual objective value : 3.00005e+00
 
 * Work counters
-  Solve time (sec)   : 2.28348e-02
+  Solve time (sec)   : 1.74539e-02
   Barrier iterations : 18

The moment matrix is as follows, we can already see the global minimizer [0, -1] from the entries (2, 1) and (3, 1). This heuristic way to obtain solutions to the polynomial optimization problem is suggested in (Laurent, 2008; (6.15)).

ν = moment_matrix(con_ref)
MomentMatrix with row/column basis:
  MonomialBasis([1, x[2], x[1], x[2]^2, x[1]*x[2], x[1]^2, x[2]^3, x[1]*x[2]^2, x[1]^2*x[2], x[1]^3, x[2]^4, x[1]*x[2]^3, x[1]^2*x[2]^2, x[1]^3*x[2], x[1]^4])
@@ -137,4 +137,4 @@
  1.2493207229285292e-8
  4.7632154656602895e-9
  4.013154592036812e-10

Even if the flatness property is not satisfied, we can still try extracting the minimizer with a low rank decomposition of rank 3. We find the optimal solution again doing so:

atomic_measure(ν, FixedRank(3))
Atomic measure on the variables x[1], x[2] with 1 atoms:
- at [-1.1555204794988076e-6, -0.9999987643852531] with weight 1.0180428801820578

This page was generated using Literate.jl.

+ at [-1.1555204794988076e-6, -0.9999987643852531] with weight 1.0180428801820578

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/min_univariate.ipynb b/dev/generated/Polynomial Optimization/min_univariate.ipynb index 3fcb165a8..5866759ae 100644 --- a/dev/generated/Polynomial Optimization/min_univariate.ipynb +++ b/dev/generated/Polynomial Optimization/min_univariate.ipynb @@ -77,95 +77,95 @@ "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" ], "image/svg+xml": [ "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" ] }, "metadata": {}, @@ -299,7 +299,7 @@ " 11 7.0000e+00 7.0000e+00 2.34e-10 3.13e-11 1.84e-12 1.72e-09 1.17e-11 9.80e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 4.14ms\n", + "solve time = 3.46ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -315,7 +315,7 @@ " Dual objective value : -7.00000e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 4.14233e-03\n", + " Solve time (sec) : 3.46367e-03\n", " Barrier iterations : 11\n", "\n" ] @@ -389,7 +389,7 @@ " 15 6.6667e+00 6.6667e+00 2.63e-09 1.69e-11 4.96e-13 1.76e-08 2.79e-12 9.70e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 29.9ms\n", + "solve time = 9.72ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -405,7 +405,7 @@ " Dual objective value : -6.66667e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 2.99364e-02\n", + " Solve time (sec) : 9.72491e-03\n", " Barrier iterations : 15\n", "\n" ] @@ -483,7 +483,7 @@ " 20 5.5080e+00 5.5080e+00 1.09e-09 1.63e-12 2.93e-14 6.04e-09 1.09e-13 9.79e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 45.5ms\n", + "solve time = 34.2ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -499,7 +499,7 @@ " Dual objective value : -5.50801e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 4.55063e-02\n", + " Solve time (sec) : 3.41637e-02\n", " Barrier iterations : 20\n", "\n" ] @@ -583,97 +583,97 @@ "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" ], "image/svg+xml": [ "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" ] }, "metadata": {}, diff --git a/dev/generated/Polynomial Optimization/min_univariate/6cae52cd.svg b/dev/generated/Polynomial Optimization/min_univariate/82ca8bc1.svg similarity index 85% rename from dev/generated/Polynomial Optimization/min_univariate/6cae52cd.svg rename to dev/generated/Polynomial Optimization/min_univariate/82ca8bc1.svg index 982d374fc..ed0c26838 100644 --- a/dev/generated/Polynomial Optimization/min_univariate/6cae52cd.svg +++ b/dev/generated/Polynomial Optimization/min_univariate/82ca8bc1.svg @@ -1,46 +1,46 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/generated/Polynomial Optimization/min_univariate/1d3ce0c3.svg b/dev/generated/Polynomial Optimization/min_univariate/e9f694f5.svg similarity index 85% rename from dev/generated/Polynomial Optimization/min_univariate/1d3ce0c3.svg rename to dev/generated/Polynomial Optimization/min_univariate/e9f694f5.svg index 35a3df6a5..1db67e288 100644 --- a/dev/generated/Polynomial Optimization/min_univariate/1d3ce0c3.svg +++ b/dev/generated/Polynomial Optimization/min_univariate/e9f694f5.svg @@ -1,45 +1,45 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/generated/Polynomial Optimization/min_univariate/index.html b/dev/generated/Polynomial Optimization/min_univariate/index.html index 1a6fadb79..a76285a02 100644 --- a/dev/generated/Polynomial Optimization/min_univariate/index.html +++ b/dev/generated/Polynomial Optimization/min_univariate/index.html @@ -17,7 +17,7 @@ using Plots plot(xs, f1.(xs), label = "f1") plot!(xs, f2.(xs), label = "f2") -plot!(xs, 4 * ones(length(xs)), label = nothing)Example block output

We will now see how to find the optimal solution using Sum of Squares Programming. We first need to pick an SDP solver, see here for a list of the available choices.

import Clarabel
+plot!(xs, 4 * ones(length(xs)), label = nothing)
Example block output

We will now see how to find the optimal solution using Sum of Squares Programming. We first need to pick an SDP solver, see here for a list of the available choices.

import Clarabel
 solver = Clarabel.Optimizer
Clarabel.MOIwrapper.Optimizer

A Sum-of-Squares certificate that $p \ge \alpha$ over the domain S, ensures that $\alpha$ is a lower bound to the polynomial optimization problem. The following function searches for the largest lower bound and finds zero using the dth level of the hierarchy`.

function solve(d)
     model = SOSModel(solver)
     @variable(model, α)
@@ -68,7 +68,7 @@
  11   7.0000e+00   7.0000e+00  2.34e-10  3.13e-11  1.84e-12  1.72e-09  1.17e-11  9.80e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 3.31ms
+solve time = 3.34ms
 * Solver : Clarabel
 
 * Status
@@ -84,7 +84,7 @@
   Dual objective value : -7.00000e+00
 
 * Work counters
-  Solve time (sec)   : 3.31385e-03
+  Solve time (sec)   : 3.33577e-03
   Barrier iterations : 11

The second level improves the lower bound

model5 = solve(5)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -132,7 +132,7 @@
  15   6.6667e+00   6.6667e+00  2.63e-09  1.69e-11  4.96e-13  1.76e-08  2.79e-12  9.70e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 29.0ms
+solve time = 25.6ms
 * Solver : Clarabel
 
 * Status
@@ -148,7 +148,7 @@
   Dual objective value : -6.66667e+00
 
 * Work counters
-  Solve time (sec)   : 2.90189e-02
+  Solve time (sec)   : 2.55892e-02
   Barrier iterations : 15

The third level finds the optimal objective value as lower bound...

model7 = solve(7)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -200,7 +200,7 @@
  20   5.5080e+00   5.5080e+00  1.09e-09  1.63e-12  2.93e-14  6.04e-09  1.09e-13  9.79e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 34.5ms
+solve time = 34.6ms
 * Solver : Clarabel
 
 * Status
@@ -216,8 +216,8 @@
   Dual objective value : -5.50801e+00
 
 * Work counters
-  Solve time (sec)   : 3.45054e-02
+  Solve time (sec)   : 3.45654e-02
   Barrier iterations : 20

...and proves it by exhibiting the minimizer.

ν7 = moment_matrix(model7[:c])
 η = atomic_measure(ν7, 1e-3) # Returns nothing as the dual is not atomic
Atomic measure on the variables x[1], x[2] with 1 atoms:
  at [2.329520151218628, 3.178493153833861] with weight 0.9999999590079649

We can indeed verify that the objective value at x_opt is equal to the lower bound.

x_opt = η.atoms[1].center
-p(x_opt)
-5.508013305052489

We can see visualize the solution as follows:

scatter!([x_opt[1]], [x_opt[2]], markershape = :star, label = nothing)
Example block output

This page was generated using Literate.jl.

+p(x_opt)
-5.508013305052489

We can see visualize the solution as follows:

scatter!([x_opt[1]], [x_opt[2]], markershape = :star, label = nothing)
Example block output

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/polynomial_optimization.ipynb b/dev/generated/Polynomial Optimization/polynomial_optimization.ipynb index b3419fb41..488f7ce5e 100644 --- a/dev/generated/Polynomial Optimization/polynomial_optimization.ipynb +++ b/dev/generated/Polynomial Optimization/polynomial_optimization.ipynb @@ -176,7 +176,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Ipopt\n\n* Status\n Result count : 1\n Termination status : LOCALLY_SOLVED\n Message from the solver:\n \"Solve_Succeeded\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.50000e-01\n Dual objective value : 7.50000e-01\n\n* Work counters\n Solve time (sec) : 7.62279e-02\n Barrier iterations : 13\n" + "text/plain": "* Solver : Ipopt\n\n* Status\n Result count : 1\n Termination status : LOCALLY_SOLVED\n Message from the solver:\n \"Solve_Succeeded\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.50000e-01\n Dual objective value : 7.50000e-01\n\n* Work counters\n Solve time (sec) : 7.59060e-02\n Barrier iterations : 13\n" }, "metadata": {}, "execution_count": 3 @@ -280,7 +280,7 @@ "Number of equality constraint Jacobian evaluations = 0\n", "Number of inequality constraint Jacobian evaluations = 1\n", "Number of Lagrangian Hessian evaluations = 13\n", - "Total seconds in IPOPT = 0.074\n", + "Total seconds in IPOPT = 0.073\n", "\n", "EXIT: Optimal Solution Found.\n" ] @@ -329,7 +329,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Ipopt\n\n* Status\n Result count : 1\n Termination status : LOCALLY_SOLVED\n Message from the solver:\n \"Solve_Succeeded\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.50000e-01\n Dual objective value : 7.50000e-01\n\n* Work counters\n Solve time (sec) : 7.43911e-02\n Barrier iterations : 13\n" + "text/plain": "* Solver : Ipopt\n\n* Status\n Result count : 1\n Termination status : LOCALLY_SOLVED\n Message from the solver:\n \"Solve_Succeeded\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.50000e-01\n Dual objective value : 7.50000e-01\n\n* Work counters\n Solve time (sec) : 7.33910e-02\n Barrier iterations : 13\n" }, "metadata": {}, "execution_count": 6 @@ -434,12 +434,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 1.90e+01 1.01e+00 5.26e+01 -2.61e+01 1.00e-01 1.60e-04 \n", - " 125| 4.27e-05 3.97e-05 9.70e-06 8.12e-06 8.63e-01 1.19e-03 \n", + " 0| 1.90e+01 1.01e+00 5.26e+01 -2.61e+01 1.00e-01 1.31e-04 \n", + " 125| 4.27e-05 3.97e-05 9.70e-06 8.12e-06 8.63e-01 1.14e-03 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 1.19e-03s = setup: 6.31e-05s + solve: 1.12e-03s\n", - "\t lin-sys: 7.46e-05s, cones: 8.83e-04s, accel: 7.42e-06s\n", + "timings: total: 1.14e-03s = setup: 6.10e-05s + solve: 1.08e-03s\n", + "\t lin-sys: 7.40e-05s, cones: 8.81e-04s, accel: 7.78e-06s\n", "------------------------------------------------------------------\n", "objective = 0.000008\n", "------------------------------------------------------------------\n" @@ -471,7 +471,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 1.29679e-05\n Dual objective value : 3.27176e-06\n\n* Work counters\n Solve time (sec) : 1.18755e-03\n" + "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 1.29679e-05\n Dual objective value : 3.27176e-06\n\n* Work counters\n Solve time (sec) : 1.13957e-03\n" }, "metadata": {}, "execution_count": 10 @@ -563,12 +563,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 1.90e+01 1.01e+00 5.26e+01 -2.61e+01 1.00e-01 1.63e-04 \n", - " 125| 4.27e-05 3.97e-05 9.70e-06 8.12e-06 8.63e-01 1.17e-03 \n", + " 0| 1.90e+01 1.01e+00 5.26e+01 -2.61e+01 1.00e-01 1.58e-04 \n", + " 125| 4.27e-05 3.97e-05 9.70e-06 8.12e-06 8.63e-01 1.16e-03 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 1.17e-03s = setup: 6.96e-05s + solve: 1.10e-03s\n", - "\t lin-sys: 7.36e-05s, cones: 8.83e-04s, accel: 7.58e-06s\n", + "timings: total: 1.16e-03s = setup: 6.48e-05s + solve: 1.10e-03s\n", + "\t lin-sys: 7.38e-05s, cones: 8.80e-04s, accel: 7.43e-06s\n", "------------------------------------------------------------------\n", "objective = 0.000008\n", "------------------------------------------------------------------\n" @@ -598,7 +598,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "MomentMatrix with row/column basis:\n MonomialBasis([1, y, x])\nAnd entries in a 3×3 SymMatrix{Float64}:\n 0.9999988622359893 0.4999978058971185 0.49999780589712745\n 0.4999978058971185 0.4999205453112 7.563537032942341e-5\n 0.49999780589712745 7.563537032942341e-5 0.49992054531120916" + "text/plain": "MomentMatrix with row/column basis:\n MonomialBasis([1, y, x])\nAnd entries in a 3×3 SymMatrix{Float64}:\n 0.9999988622359886 0.499997805897128 0.4999978058971182\n 0.499997805897128 0.49992054531121116 7.563537032846814e-5\n 0.4999978058971182 7.563537032846814e-5 0.4999205453112012" }, "metadata": {}, "execution_count": 13 @@ -643,12 +643,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 1.06e+01 4.30e-01 3.19e+01 -1.57e+01 1.00e-01 1.76e-04 \n", - " 125| 2.44e-04 2.14e-05 1.20e-05 -4.90e-05 1.00e-01 1.70e-03 \n", + " 0| 1.06e+01 4.30e-01 3.19e+01 -1.57e+01 1.00e-01 1.72e-04 \n", + " 125| 2.44e-04 2.14e-05 1.20e-05 -4.90e-05 1.00e-01 1.72e-03 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 1.70e-03s = setup: 7.49e-05s + solve: 1.63e-03s\n", - "\t lin-sys: 1.09e-04s, cones: 1.32e-03s, accel: 4.77e-05s\n", + "timings: total: 1.72e-03s = setup: 7.31e-05s + solve: 1.65e-03s\n", + "\t lin-sys: 1.24e-04s, cones: 1.32e-03s, accel: 4.75e-05s\n", "------------------------------------------------------------------\n", "objective = -0.000049\n", "------------------------------------------------------------------\n" @@ -683,7 +683,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : -4.29823e-05\n Dual objective value : -5.49868e-05\n\n* Work counters\n Solve time (sec) : 1.70327e-03\n" + "text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : -4.29823e-05\n Dual objective value : -5.49868e-05\n\n* Work counters\n Solve time (sec) : 1.72016e-03\n" }, "metadata": {}, "execution_count": 15 @@ -708,7 +708,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "MomentMatrix with row/column basis:\n MonomialBasis([1, y, x, y^2, x*y, x^2])\nAnd entries in a 6×6 SymMatrix{Float64}:\n 1.0000084649794825 0.5001118271564037 … 0.5003336181952718\n 0.5001118271564037 0.5003460975048496 -8.014565849892654e-5\n 0.5001118271564211 -0.00012664913635681752 0.5004463755229258\n 0.5003336181952563 0.5004463755229072 1.952914136044117\n -0.00012729223310789853 -9.194362988273727e-5 -1.8561449853462573\n 0.5003336181952718 -8.014565849892654e-5 … 8.524707147814208" + "text/plain": "MomentMatrix with row/column basis:\n MonomialBasis([1, y, x, y^2, x*y, x^2])\nAnd entries in a 6×6 SymMatrix{Float64}:\n 1.0000084649794725 0.5001118271564022 … 0.5003336181951871\n 0.5001118271564022 0.5003460975048036 -8.014565847954353e-5\n 0.500111827156384 -0.00012664913632612457 0.5004463755228061\n 0.5003336181952058 0.5004463755228333 1.9529141360442046\n -0.00012729223307556169 -9.194362986569672e-5 -1.8561449853461915\n 0.5003336181951871 -8.014565847954353e-5 … 8.524707147814137" }, "metadata": {}, "execution_count": 16 @@ -733,7 +733,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "6-element Vector{Float64}:\n 11.29213708208392\n 6.61278028163044\n 1.5788661771503743\n 1.059760066060781\n 0.45948547678087936\n 4.487072183230438e-16" + "text/plain": "6-element Vector{Float64}:\n 11.292137082083903\n 6.612780281630263\n 1.5788661771503947\n 1.059760066060844\n 0.45948547678080226\n 2.306276178067672e-16" }, "metadata": {}, "execution_count": 17 @@ -759,7 +759,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "Atomic measure on the variables x, y with 1 atoms:\n at [0.5000778765243163, 0.5001018243812723] with weight 1.6079422332661455" + "text/plain": "Atomic measure on the variables x, y with 1 atoms:\n at [0.5000778765242776, 0.5001018243812856] with weight 1.6079422332660873" }, "metadata": {}, "execution_count": 18 @@ -802,12 +802,12 @@ "------------------------------------------------------------------\n", " iter | pri res | dua res | gap | obj | scale | time (s)\n", "------------------------------------------------------------------\n", - " 0| 2.21e+01 1.35e+00 3.74e+01 -1.86e+01 1.00e-01 2.03e-04 \n", - " 175| 7.26e-05 8.28e-06 2.10e-05 -1.57e-05 1.00e-01 2.49e-03 \n", + " 0| 2.21e+01 1.35e+00 3.74e+01 -1.86e+01 1.00e-01 2.01e-04 \n", + " 175| 7.26e-05 8.28e-06 2.10e-05 -1.57e-05 1.00e-01 2.46e-03 \n", "------------------------------------------------------------------\n", "status: solved\n", - "timings: total: 2.49e-03s = setup: 9.88e-05s + solve: 2.39e-03s\n", - "\t lin-sys: 2.43e-04s, cones: 1.86e-03s, accel: 6.03e-05s\n", + "timings: total: 2.47e-03s = setup: 9.65e-05s + solve: 2.37e-03s\n", + "\t lin-sys: 2.44e-04s, cones: 1.85e-03s, accel: 5.75e-05s\n", "------------------------------------------------------------------\n", "objective = -0.000016\n", "------------------------------------------------------------------\n" @@ -834,7 +834,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : SCS\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.61826e-05\n Dual objective value : 5.20758e-06\n\n* Work counters\n Solve time (sec) : 2.49076e-03\n" + "text/plain": "* Solver : SCS\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.61826e-05\n Dual objective value : 5.20758e-06\n\n* Work counters\n Solve time (sec) : 2.46561e-03\n" }, "metadata": {}, "execution_count": 20 @@ -912,7 +912,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "Atomic measure on the variables x, y with 2 atoms:\n at [0.9946508364409372, 0.005346125382867941] with weight 0.5511753483416818\n at [-0.011834484693471703, 1.0118314465172766] with weight 0.5285747070034233" + "text/plain": "Atomic measure on the variables x, y with 2 atoms:\n at [0.9946508364409377, 0.0053461253828677845] with weight 0.5511753483416815\n at [-0.011834484693471814, 1.011831446517277] with weight 0.5285747070034227" }, "metadata": {}, "execution_count": 23 @@ -1026,7 +1026,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "2-element Vector{Vector{Float64}}:\n [0.9946508364409374, 0.0053461253828677065]\n [-0.01183448469347198, 1.011831446517277]" + "text/plain": "2-element Vector{Vector{Float64}}:\n [0.9946508364409373, 0.005346125382867784]\n [-0.01183448469347187, 1.0118314465172766]" }, "metadata": {}, "execution_count": 27 @@ -1090,7 +1090,7 @@ "\n", "\n", "\n", - "\r\u001b[K\u001b[A\r\u001b[K\u001b[A\r\u001b[K\u001b[A\r\u001b[K\u001b[A\rTracking 4 paths... 100%|███████████████████████████████| Time: 0:00:18\u001b[K\r\n", + "\r\u001b[K\u001b[A\r\u001b[K\u001b[A\r\u001b[K\u001b[A\r\u001b[K\u001b[A\rTracking 4 paths... 100%|███████████████████████████████| Time: 0:00:17\u001b[K\r\n", " # paths tracked: 4\u001b[K\r\n", " # non-singular solutions (real): 0 (0)\u001b[K\r\n", " # singular endpoints (real): 0 (0)\u001b[K\r\n", @@ -1100,7 +1100,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "Atomic measure on the variables x, y with 2 atoms:\n at [1.0118921928175115, -0.0017691904220478618] with weight 0.5285176504040905\n at [-0.006730758038636695, 0.9838700948175931] with weight 0.5604265409211654" + "text/plain": "Atomic measure on the variables x, y with 2 atoms:\n at [1.0087400357050913, 0.0027235425989198194] with weight 0.5336596629892292\n at [-0.019129954926696707, 0.9876200600922921] with weight 0.5548417744977788" }, "metadata": {}, "execution_count": 28 @@ -1156,7 +1156,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "4-element Vector{HomotopyContinuation.PathResult}:\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[1.0000398617446289 - 0.009525169841688571im, 0.0073574794956642355 - 0.0006490641009926352im]\n • accuracy → 0.028563\n • residual → 0.012839\n • condition_jacobian → 7.0979\n • steps → 37 / 0\n • extended_precision → false\n • path_number → 1\n\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[-0.2739822599364022 - 2.212678488560979im, 0.35216630608604266 + 0.022187553983331842im]\n • accuracy → 5.3956\n • residual → 1.2803\n • condition_jacobian → 2.8564\n • steps → 36 / 0\n • extended_precision → false\n • path_number → 2\n\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[3.8289867987848907 + 55.466487875338395im, 4.489939079099477 + 57.7056158488816im]\n • accuracy → 257.47\n • residual → 33.164\n • condition_jacobian → 116.57\n • steps → 26 / 0\n • extended_precision → false\n • path_number → 3\n\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[-0.011721959565525655 + 0.010044034590264653im, 1.0143419279838466 + 0.005616922375607034im]\n • accuracy → 0.036051\n • residual → 0.0096874\n • condition_jacobian → 15.521\n • steps → 26 / 0\n • extended_precision → false\n • path_number → 4\n" + "text/plain": "4-element Vector{HomotopyContinuation.PathResult}:\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[0.6421385561770792 - 0.08860303121175886im, 0.127897974185849 - 0.5152113183332582im]\n • accuracy → 1.0552\n • residual → 0.54686\n • condition_jacobian → 4.1551\n • steps → 31 / 0\n • extended_precision → false\n • path_number → 1\n\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[1.0371024575390335 + 0.0008941337441332816im, 0.004948952793982149 + 0.03493581741672401im]\n • accuracy → 0.090224\n • residual → 0.034302\n • condition_jacobian → 27.62\n • steps → 23 / 0\n • extended_precision → false\n • path_number → 2\n\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[0.01029112662000238 + 0.0053151244973309465im, 1.0110030088102833 - 0.011090323582558133im]\n • accuracy → 0.036036\n • residual → 0.022983\n • condition_jacobian → 14.649\n • steps → 22 / 0\n • extended_precision → false\n • path_number → 3\n\n PathResult:\n • return_code → :excess_solution\n • solution → ComplexF64[3.400692877684158 + 34.28049377236793im, 2.854554576052273 + 33.87212885443248im]\n • accuracy → 111.63\n • residual → 22.764\n • condition_jacobian → 103.61\n • steps → 28 / 0\n • extended_precision → false\n • path_number → 4\n" }, "metadata": {}, "execution_count": 29 diff --git a/dev/generated/Polynomial Optimization/polynomial_optimization/index.html b/dev/generated/Polynomial Optimization/polynomial_optimization/index.html index c6b337747..b1e74b046 100644 --- a/dev/generated/Polynomial Optimization/polynomial_optimization/index.html +++ b/dev/generated/Polynomial Optimization/polynomial_optimization/index.html @@ -69,7 +69,7 @@ Number of equality constraint Jacobian evaluations = 0 Number of inequality constraint Jacobian evaluations = 1 Number of Lagrangian Hessian evaluations = 13 -Total seconds in IPOPT = 1.418 +Total seconds in IPOPT = 1.388 EXIT: Optimal Solution Found.

As we can see below, the termination status is LOCALLY_SOLVED and not of OPTIMAL because Ipopt only guarantees local optimality.

solution_summary(model)
* Solver : Ipopt
 
@@ -86,7 +86,7 @@
   Dual objective value : 7.50000e-01
 
 * Work counters
-  Solve time (sec)   : 1.41850e+00
+  Solve time (sec)   : 1.38847e+00
   Barrier iterations : 13

Indeed, the solution found is not globally optimal:

value(a), value(b)
(0.49999999667062867, 0.4999999966705758)

Note that the problem can be written equivalently as follows using registered functions. The difference is that the gradient and hessian will be computed via the Symbolic Differentiation provided by MultivariatePolynomials instead of JuMP's Automatic Differentiation:

f(a, b) = p(x => a, y => b)
 ∇p = differentiate(p, [x, y])
@@ -161,7 +161,7 @@
 Number of equality constraint Jacobian evaluations   = 0
 Number of inequality constraint Jacobian evaluations = 1
 Number of Lagrangian Hessian evaluations             = 13
-Total seconds in IPOPT                               = 0.043
+Total seconds in IPOPT                               = 0.042
 
 EXIT: Optimal Solution Found.

Even if we have the algebraic expressions of gradient and hessian, Ipopt is not using these symbolic expressions but only local information hence it can still only provide local guarantees:

solution_summary(gmodel)
* Solver : Ipopt
 
@@ -178,7 +178,7 @@
   Dual objective value : 7.50000e-01
 
 * Work counters
-  Solve time (sec)   : 4.38809e-02
+  Solve time (sec)   : 4.23980e-02
   Barrier iterations : 13

and the same solution is found:

value(a), value(b)
(0.49999999667062867, 0.4999999966705758)

Sum-of-Squares approach

We will now see how to find the optimal solution using Sum of Squares Programming. We first need to pick an SDP solver, see here for a list of the available choices.

import SCS
 scs = SCS.Optimizer
@@ -204,12 +204,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.90e+01  1.01e+00  5.26e+01 -2.61e+01  1.00e-01  1.73e-04
+     0| 1.90e+01  1.01e+00  5.26e+01 -2.61e+01  1.00e-01  1.71e-04
    125| 4.27e-05  3.97e-05  9.70e-06  8.12e-06  8.63e-01  1.19e-03
 ------------------------------------------------------------------
 status:  solved
-timings: total: 1.19e-03s = setup: 8.06e-05s + solve: 1.11e-03s
-	 lin-sys: 7.42e-05s, cones: 8.95e-04s, accel: 7.34e-06s
+timings: total: 1.19e-03s = setup: 8.12e-05s + solve: 1.11e-03s
+	 lin-sys: 7.43e-05s, cones: 8.78e-04s, accel: 7.66e-06s
 ------------------------------------------------------------------
 objective = 0.000008
 ------------------------------------------------------------------

This time, the termination status is OPTIMAL but this does not necessarily mean that we found the optimal solution to the polynomial optimization problem. This only means that CSDP founds an optimal solution to the Sum-of-Squares relaxation.

solution_summary(model)
* Solver : Dual model with SCS attached
@@ -227,7 +227,7 @@
   Dual objective value : 3.27176e-06
 
 * Work counters
-  Solve time (sec)   : 1.19359e-03
+  Solve time (sec)   : 1.19474e-03

The feasibility of the primal solution guarantees that the objective value 0 is a lower bound to the polynomial optimization problem. The optimality means that it's the best lower bound we can get (at this degree of the hierarcy). Using the solution $(1/2, 1/2)$ found by Ipopt of objective value $1/4$ and this certificate of lower bound $0$ we know that the optimal objective value is in the interval $[0, 1/4]$ but we still do not know what it is (if we consider that we did not try the solutions $(1, 0)$ and $(0, 1)$ as done in the introduction). If the dual of the constraint c3 was atomic, its atoms would have given optimal solutions of objective value $0$ but that is not the case.

ν3 = moment_matrix(c3)
 atomic_measure(ν3, 1e-3) # Returns nothing as the dual is not atomic

Fortunately, there is a hierarchy of programs with increasingly better bounds that can be solved until we get one with atom dual variables. This comes from the way the Sum-of-Squares constraint with domain S is formulated. The polynomial $p - \alpha$ is guaranteed to be nonnegative over the domain S if there exists Sum-of-Squares polynomials $s_0$, $s_1$, $s_2$, $s_3$ such that

\[p - \alpha = s_0 + s_1 x + s_2 y + s_3 (x + y - 1).\]

Indeed, in the domain S, $x$, $y$ and $x + y - 1$ are nonnegative so the right-hand side is a sum of squares hence is nonnegative. Once the degrees of $s_1$, $s_2$ and $s_3$ have been decided, the degree needed for $s_0$ will be determined but we have a freedom in choosing the degrees of $s_1$, $s_2$ and $s_3$. By default, they are chosen so that the degrees of $s_1 x$, $s_2 y$ and $s_3 (x + y - 1)$ match those of $p - \alpha$ but this can be overwritten using the maxdegree keyword argument.

The maxdegree keyword argument

The maximum total degree (i.e. maximum sum of the exponents of $x$ and $y$) of the monomials of $p$ is 3 so the constraint in the program above is equivalent to @constraint(model, p >= α, domain = S, maxdegree = 3). That is, since $x$, $y$ and $x + y - 1$ have total degree 1, the sum of squares polynomials $s_1$, $s_2$ and $s_3$ have been chosen with maximum total degree $2$. Since these polynomials are sums of squares, their degree must be even so the next maximum total degree to try is 4. For this reason, the keywords maxdegree = 4 and maxdegree = 5 have the same effect in this example. In general, if the polynomials in the domain are not all odd or all even, each value of maxdegree has a different effect in the choice of the maximum total degree of some $s_i$.

model = SOSModel(dual_scs)
 @variable(model, α)
@@ -250,20 +250,20 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.90e+01  1.01e+00  5.26e+01 -2.61e+01  1.00e-01  1.73e-04
-   125| 4.27e-05  3.97e-05  9.70e-06  8.12e-06  8.63e-01  1.20e-03
+     0| 1.90e+01  1.01e+00  5.26e+01 -2.61e+01  1.00e-01  1.58e-04
+   125| 4.27e-05  3.97e-05  9.70e-06  8.12e-06  8.63e-01  1.18e-03
 ------------------------------------------------------------------
 status:  solved
-timings: total: 1.20e-03s = setup: 7.80e-05s + solve: 1.12e-03s
-	 lin-sys: 7.45e-05s, cones: 8.85e-04s, accel: 7.43e-06s
+timings: total: 1.19e-03s = setup: 7.14e-05s + solve: 1.11e-03s
+	 lin-sys: 7.47e-05s, cones: 9.00e-04s, accel: 7.66e-06s
 ------------------------------------------------------------------
 objective = 0.000008
 ------------------------------------------------------------------

We can see that the basis of the moment matrix didn't increase:

moment_matrix(c4)
MomentMatrix with row/column basis:
  MonomialBasis([1, y, x])
 And entries in a 3×3 SymMatrix{Float64}:
- 0.9999988622359893   0.4999978058971185    0.49999780589712745
- 0.4999978058971185   0.4999205453112       7.563537032942341e-5
- 0.49999780589712745  7.563537032942341e-5  0.49992054531120916

This is because of the Newton polytope reduction that determined that gram matrix will be zero for these degrees so it reduced the problem back to the equivalent of maxdegree 3 Let's turn this off with newton_polytope = nothing

function sos(solver, deg)
+ 0.9999988622359886  0.499997805897128     0.4999978058971182
+ 0.499997805897128   0.49992054531121116   7.563537032846814e-5
+ 0.4999978058971182  7.563537032846814e-5  0.4999205453112012

This is because of the Newton polytope reduction that determined that gram matrix will be zero for these degrees so it reduced the problem back to the equivalent of maxdegree 3 Let's turn this off with newton_polytope = nothing

function sos(solver, deg)
     model = SOSModel(solver)
     @variable(model, α)
     @objective(model, Max, α)
@@ -288,12 +288,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 1.06e+01  4.30e-01  3.19e+01 -1.57e+01  1.00e-01  1.73e-04
-   125| 2.44e-04  2.14e-05  1.20e-05 -4.90e-05  1.00e-01  1.68e-03
+     0| 1.06e+01  4.30e-01  3.19e+01 -1.57e+01  1.00e-01  1.74e-04
+   125| 2.44e-04  2.14e-05  1.20e-05 -4.90e-05  1.00e-01  1.70e-03
 ------------------------------------------------------------------
 status:  solved
-timings: total: 1.68e-03s = setup: 7.57e-05s + solve: 1.60e-03s
-	 lin-sys: 1.10e-04s, cones: 1.32e-03s, accel: 2.60e-05s
+timings: total: 1.70e-03s = setup: 7.32e-05s + solve: 1.63e-03s
+	 lin-sys: 1.11e-04s, cones: 1.34e-03s, accel: 2.69e-05s
 ------------------------------------------------------------------
 objective = -0.000049
 ------------------------------------------------------------------

We see that the lower bound is still 0:

solution_summary(dual_model4)
* Solver : Dual model with SCS attached
@@ -311,24 +311,24 @@
   Dual objective value : -5.49868e-05
 
 * Work counters
-  Solve time (sec)   : 1.67993e-03
+  Solve time (sec)   : 1.70419e-03

Let's now look at which solution we can extract from the moment matrix:

dual_ν4 = moment_matrix(dual_model4[:c])
MomentMatrix with row/column basis:
  MonomialBasis([1, y, x, y^2, x*y, x^2])
 And entries in a 6×6 SymMatrix{Float64}:
-  1.0000084649794825       0.5001118271564037      …   0.5003336181952718
-  0.5001118271564037       0.5003460975048496         -8.014565849892654e-5
-  0.5001118271564211      -0.00012664913635681752      0.5004463755229258
-  0.5003336181952563       0.5004463755229072          1.952914136044117
- -0.00012729223310789853  -9.194362988273727e-5       -1.8561449853462573
-  0.5003336181952718      -8.014565849892654e-5    …   8.524707147814208

Looking at the singular values, 4 seems to be a reasonable rank:

using LinearAlgebra
+  1.0000084649794725       0.5001118271564022      …   0.5003336181951871
+  0.5001118271564022       0.5003460975048036         -8.014565847954353e-5
+  0.500111827156384       -0.00012664913632612457      0.5004463755228061
+  0.5003336181952058       0.5004463755228333          1.9529141360442046
+ -0.00012729223307556169  -9.194362986569672e-5       -1.8561449853461915
+  0.5003336181951871      -8.014565847954353e-5    …   8.524707147814137

Looking at the singular values, 4 seems to be a reasonable rank:

using LinearAlgebra
 svdvals(Matrix(dual_ν4.Q))
6-element Vector{Float64}:
- 11.29213708208392
-  6.61278028163044
-  1.5788661771503743
-  1.059760066060781
-  0.45948547678087936
-  4.487072183230438e-16

The solution we extract is (0.5, 0.5) which is the solution found by Ipopt:

atomic_measure(dual_ν4, FixedRank(4))
Atomic measure on the variables x, y with 1 atoms:
- at [0.5000778765243163, 0.5001018243812723] with weight 1.6079422332661455

This process is quite sensitive numerically so let's try to solve it without dualization as well:

model4 = sos(scs, 4)
------------------------------------------------------------------
+ 11.292137082083903
+  6.612780281630263
+  1.5788661771503947
+  1.059760066060844
+  0.45948547678080226
+  2.306276178067672e-16

The solution we extract is (0.5, 0.5) which is the solution found by Ipopt:

atomic_measure(dual_ν4, FixedRank(4))
Atomic measure on the variables x, y with 1 atoms:
+ at [0.5000778765242776, 0.5001018243812856] with weight 1.6079422332660873

This process is quite sensitive numerically so let's try to solve it without dualization as well:

model4 = sos(scs, 4)
------------------------------------------------------------------
 	       SCS v3.2.4 - Splitting Conic Solver
 	(c) Brendan O'Donoghue, Stanford University, 2012
 ------------------------------------------------------------------
@@ -345,12 +345,12 @@
 ------------------------------------------------------------------
  iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
 ------------------------------------------------------------------
-     0| 2.21e+01  1.35e+00  3.74e+01 -1.86e+01  1.00e-01  1.98e-04
+     0| 2.21e+01  1.35e+00  3.74e+01 -1.86e+01  1.00e-01  2.12e-04
    175| 7.26e-05  8.28e-06  2.10e-05 -1.57e-05  1.00e-01  2.48e-03
 ------------------------------------------------------------------
 status:  solved
-timings: total: 2.49e-03s = setup: 9.96e-05s + solve: 2.39e-03s
-	 lin-sys: 2.46e-04s, cones: 1.86e-03s, accel: 5.87e-05s
+timings: total: 2.48e-03s = setup: 1.17e-04s + solve: 2.36e-03s
+	 lin-sys: 2.41e-04s, cones: 1.85e-03s, accel: 5.93e-05s
 ------------------------------------------------------------------
 objective = -0.000016
 ------------------------------------------------------------------

We see that the lower bound is again 0:

solution_summary(model4)
* Solver : SCS
@@ -368,7 +368,7 @@
   Dual objective value : 5.20758e-06
 
 * Work counters
-  Solve time (sec)   : 2.48644e-03
+  Solve time (sec)   : 2.47781e-03

The moment matrix is the following

ν4 = moment_matrix(model4[:c])
MomentMatrix with row/column basis:
  MonomialBasis([1, y, x, y^2, x*y, x^2])
 And entries in a 6×6 SymMatrix{Float64}:
@@ -384,8 +384,8 @@
  0.019380459836853832
  0.016994381823767828
  5.714524905397067e-16

This time, the dual variable is atomic as it is the moments of the measure $0.5 \delta(x-1, y) + 0.5 \delta(x, y-1)$ where $\delta(x, y)$ is the dirac measure centered at $(0, 0)$. Therefore the program provides both a certificate that $0$ is a lower bound and a certificate that it is also an upper bound since it is attained at the global minimizers $(1, 0)$ and $(0, 1)$.

atomic_measure(ν4, FixedRank(3))
Atomic measure on the variables x, y with 2 atoms:
- at [0.9946508364409377, 0.005346125382867864] with weight 0.5511753483416815
- at [-0.011834484693471758, 1.011831446517277] with weight 0.5285747070034227

A deeper look into atom extraction

The moment matrix is transformed into a system of polynomials equations whose solutions give the atoms. This transformation uses the SVD decomposition of the moment matrix and discards the equations corresponding to the lowest singular values. When this system of equation has an infinite number of solutions, atomic_measure concludes that the measure is not atomic. For instance, with maxdegree = 3, we obtain the system $x + y = 1$ which contains a whole line of solution. This explains atomic_measure returned nothing.

ν3 = moment_matrix(c3)
+ at [0.9946508364409368, 0.005346125382867939] with weight 0.5511753483416821
+ at [-0.011834484693471647, 1.0118314465172762] with weight 0.5285747070034235

A deeper look into atom extraction

The moment matrix is transformed into a system of polynomials equations whose solutions give the atoms. This transformation uses the SVD decomposition of the moment matrix and discards the equations corresponding to the lowest singular values. When this system of equation has an infinite number of solutions, atomic_measure concludes that the measure is not atomic. For instance, with maxdegree = 3, we obtain the system $x + y = 1$ which contains a whole line of solution. This explains atomic_measure returned nothing.

ν3 = moment_matrix(c3)
 SumOfSquares.MultivariateMoments.compute_support!(ν3, LeadingRelativeRankTol(1e-3))

With maxdegree = 4, we obtain the system

\[\begin{aligned} x + y & = 1\\ y^2 & = y\\ @@ -401,51 +401,51 @@ -0.9999969618238052 + 1.0000000000000002*y + x = 0 0.005409377779409965 - 1.0171775719001446*y + y^2 = 0

The solutions of this system then give the minimizers

collect(ν4.support)
2-element Vector{Vector{Float64}}:
- [0.9946508364409369, 0.005346125382868018]
- [-0.011834484693471592, 1.0118314465172762]

The function atomic_measure then reuses the matrix of moments to find the weights $1/2$, $1/2$ corresponding to the diracs centered respectively at $(0, 1)$ and $(1, 0)$. This details how the function obtained the result $0.5 \delta(x-1, y) + 0.5 \delta(x, y-1)$ given in the previous section.

HomotopyContinuation

As discussed in the previous section, the atom extraction relies on the solution of a system of algebraic equations. The atomic_measure function takes an optional algebraic_solver argument that is used to solve this system of equation. If no solver is provided, the default solver of SemialgebraicSets.jl is used which currently computes the Gröbner basis, then the multiplication matrices and then the Schur decomposition of a random combination of these matrices. As the system of equations is obtained from a numerical solution and is represented using floating point coefficients, homotopy continuation is recommended as it is more numerically robust than Gröbner basis computation. The following uses homotopy continuation to solve the system of equations.

using HomotopyContinuation
+ [0.9946508364409374, 0.005346125382867863]
+ [-0.011834484693471814, 1.0118314465172769]

The function atomic_measure then reuses the matrix of moments to find the weights $1/2$, $1/2$ corresponding to the diracs centered respectively at $(0, 1)$ and $(1, 0)$. This details how the function obtained the result $0.5 \delta(x-1, y) + 0.5 \delta(x, y-1)$ given in the previous section.

HomotopyContinuation

As discussed in the previous section, the atom extraction relies on the solution of a system of algebraic equations. The atomic_measure function takes an optional algebraic_solver argument that is used to solve this system of equation. If no solver is provided, the default solver of SemialgebraicSets.jl is used which currently computes the Gröbner basis, then the multiplication matrices and then the Schur decomposition of a random combination of these matrices. As the system of equations is obtained from a numerical solution and is represented using floating point coefficients, homotopy continuation is recommended as it is more numerically robust than Gröbner basis computation. The following uses homotopy continuation to solve the system of equations.

using HomotopyContinuation
 algebraic_solver = SemialgebraicSetsHCSolver(; excess_residual_tol = 1e-1, real_tol = 1e-1, compile = false)
 atomic_measure(ν4, FixedRank(3), Echelon(), algebraic_solver)
Atomic measure on the variables x, y with 2 atoms:
- at [1.0168995348636667, -0.0032126978005694562] with weight 0.527124761686776
- at [-0.00822725245806747, 1.0062169670457735] with weight 0.538778794976575

As the system has 3 equations for 2 variables and the coefficients of the equations are to be treated with tolerance since they originate from the solution of an SDP, we need to set excess_residual_tol and real_tol to a high tolerance otherwise, HomotopyContinuation would consider that there is no solution. Indeed, as the system is overdetermined (it has more equations than variables) HomotopyContinuation expects to have excess solution hence it filters out excess solution among the solution found. It determines which solution are in excess by comparing the infinity norm of the residuals of the equations at the solution with excess_residual_tol. It also filters out solution for which the absolute value of the imaginary part of one of the entry is larger than real_tol and strips out the imaginary part. The raw solutions obtained by HomotopyContinuation can be obtained as follows:

F = HomotopyContinuation.System(ν4.support)
+ at [1.0122239916846751, 0.001033699360162873] with weight 0.5290248898419753
+ at [-0.011523308478269798, 0.9853143567430592] with weight 0.5584477592532018

As the system has 3 equations for 2 variables and the coefficients of the equations are to be treated with tolerance since they originate from the solution of an SDP, we need to set excess_residual_tol and real_tol to a high tolerance otherwise, HomotopyContinuation would consider that there is no solution. Indeed, as the system is overdetermined (it has more equations than variables) HomotopyContinuation expects to have excess solution hence it filters out excess solution among the solution found. It determines which solution are in excess by comparing the infinity norm of the residuals of the equations at the solution with excess_residual_tol. It also filters out solution for which the absolute value of the imaginary part of one of the entry is larger than real_tol and strips out the imaginary part. The raw solutions obtained by HomotopyContinuation can be obtained as follows:

F = HomotopyContinuation.System(ν4.support)
 res = HomotopyContinuation.solve(F, algebraic_solver.options...)
 path_results(res)
4-element Vector{HomotopyContinuation.PathResult}:
  PathResult:
  • return_code → :excess_solution
- • solution → ComplexF64[-42.865216032912045 + 10.56739690515434im, -42.71227241097873 + 9.760231307487235im]
- • accuracy → 106.35
- • residual → 27.507
- • condition_jacobian → 148.01
- • steps → 48 / 0
+ • solution → ComplexF64[-0.016767176612879256 + 0.0075836773517880636im, 0.985738924272064 - 0.005088198431288551im]
+ • accuracy → 0.03423
+ • residual → 0.024925
+ • condition_jacobian → 19.531
+ • steps → 27 / 0
  • extended_precision → false
  • path_number → 1
 
  PathResult:
  • return_code → :excess_solution
- • solution → ComplexF64[-0.0009230199646604752 + 0.002473006841600545im, 1.023317073297938 - 0.02361822751015577im]
- • accuracy → 0.036833
- • residual → 0.02722
- • condition_jacobian → 13.734
- • steps → 25 / 0
+ • solution → ComplexF64[1.00937899725859 + 0.0022282433774965795im, 0.0018996657081525906 - 0.0024223843693176312im]
+ • accuracy → 0.012409
+ • residual → 0.0042413
+ • condition_jacobian → 12.224
+ • steps → 23 / 0
  • extended_precision → false
  • path_number → 2
 
  PathResult:
  • return_code → :excess_solution
- • solution → ComplexF64[0.06152833786537611 + 0.240813126686809im, 0.22115866243072535 - 0.5314151213391687im]
- • accuracy → 0.92549
- • residual → 0.45866
- • condition_jacobian → 5.6525
+ • solution → ComplexF64[0.3284375966339261 - 2.181242638335257im, 2.467234263840134 - 2.102179751002589im]
+ • accuracy → 5.1079
+ • residual → 2.1339
+ • condition_jacobian → 4.1105
  • steps → 25 / 0
  • extended_precision → false
  • path_number → 3
 
  PathResult:
  • return_code → :excess_solution
- • solution → ComplexF64[1.0257445438768564 + 0.011926808591181724im, -0.004819846098581433 + 0.0024629605833554904im]
- • accuracy → 0.030371
- • residual → 0.020668
- • condition_jacobian → 24.246
- • steps → 17 / 0
+ • solution → ComplexF64[-5.435572407752557 - 15.802799845311156im, -3.303237613221509 - 15.736789462309966im]
+ • accuracy → 36.302
+ • residual → 14.264
+ • condition_jacobian → 76.94
+ • steps → 33 / 0
  • extended_precision → false
  • path_number → 4
-

The printed residual above shows why 1e-1 allows to filter how the 2 actual solutions from the 2 excess solutions.

This page was generated using Literate.jl.

+

The printed residual above shows why 1e-1 allows to filter how the 2 actual solutions from the 2 excess solutions.

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/qcqp.ipynb b/dev/generated/Polynomial Optimization/qcqp.ipynb index 694cb5355..d55a328e5 100644 --- a/dev/generated/Polynomial Optimization/qcqp.ipynb +++ b/dev/generated/Polynomial Optimization/qcqp.ipynb @@ -189,7 +189,7 @@ " 8 2.2618e+10 3.8076e+10 6.83e-01 1.25e-08 1.35e-09 1.55e+10 1.88e-06 9.80e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = primal infeasible\n", - "solve time = 266ms\n", + "solve time = 258ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -205,7 +205,7 @@ " Dual objective value : -3.80764e+10\n", "\n", "* Work counters\n", - " Solve time (sec) : 2.65559e-01\n", + " Solve time (sec) : 2.58241e-01\n", " Barrier iterations : 8\n", "\n" ] @@ -278,7 +278,7 @@ " 14 3.1000e+02 3.1000e+02 5.77e-09 6.12e-10 9.18e-11 1.80e-06 5.46e-09 9.73e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 43.0ms\n", + "solve time = 42.0ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -294,7 +294,7 @@ " Dual objective value : -3.10000e+02\n", "\n", "* Work counters\n", - " Solve time (sec) : 4.29614e-02\n", + " Solve time (sec) : 4.20184e-02\n", " Barrier iterations : 14\n", "\n" ] diff --git a/dev/generated/Polynomial Optimization/qcqp/index.html b/dev/generated/Polynomial Optimization/qcqp/index.html index d2354567c..7e192e77f 100644 --- a/dev/generated/Polynomial Optimization/qcqp/index.html +++ b/dev/generated/Polynomial Optimization/qcqp/index.html @@ -82,7 +82,7 @@ 8 2.2618e+10 3.8076e+10 6.83e-01 1.25e-08 1.35e-09 1.55e+10 1.88e-06 9.80e-01 --------------------------------------------------------------------------------------------- Terminated with status = primal infeasible -solve time = 2.43ms +solve time = 2.35ms * Solver : Clarabel * Status @@ -98,7 +98,7 @@ Dual objective value : -3.80764e+10 * Work counters - Solve time (sec) : 2.42646e-03 + Solve time (sec) : 2.35432e-03 Barrier iterations : 8

The second level of the hierarchy finds the lower bound of -310.

model3 = solve(4)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -145,7 +145,7 @@
  14   3.1000e+02   3.1000e+02  5.77e-09  6.12e-10  9.18e-11  1.80e-06  5.46e-09  9.73e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 42.5ms
+solve time = 41.4ms
 * Solver : Clarabel
 
 * Status
@@ -161,5 +161,5 @@
   Dual objective value : -3.10000e+02
 
 * Work counters
-  Solve time (sec)   : 4.24602e-02
-  Barrier iterations : 14

This page was generated using Literate.jl.

+ Solve time (sec) : 4.14299e-02 + Barrier iterations : 14

This page was generated using Literate.jl.

diff --git a/dev/generated/Polynomial Optimization/qp.ipynb b/dev/generated/Polynomial Optimization/qp.ipynb index d33797412..140886785 100644 --- a/dev/generated/Polynomial Optimization/qp.ipynb +++ b/dev/generated/Polynomial Optimization/qp.ipynb @@ -173,7 +173,7 @@ " 5 1.8390e+10 2.0786e+10 1.30e-01 2.05e-07 2.78e-08 2.40e+09 3.71e-05 9.86e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = primal infeasible\n", - "solve time = 1.61ms\n", + "solve time = 3.46ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -189,7 +189,7 @@ " Dual objective value : -2.07856e+10\n", "\n", "* Work counters\n", - " Solve time (sec) : 1.61461e-03\n", + " Solve time (sec) : 3.46474e-03\n", " Barrier iterations : 5\n", "\n" ] @@ -264,7 +264,7 @@ " 11 2.2000e+01 2.2000e+01 3.49e-10 7.90e-11 1.92e-11 8.30e-09 3.83e-09 9.88e-01 \n", "---------------------------------------------------------------------------------------------\n", "Terminated with status = solved\n", - "solve time = 12.9ms\n", + "solve time = 43.7ms\n", "* Solver : Clarabel\n", "\n", "* Status\n", @@ -280,7 +280,7 @@ " Dual objective value : -2.20000e+01\n", "\n", "* Work counters\n", - " Solve time (sec) : 1.28867e-02\n", + " Solve time (sec) : 4.36733e-02\n", " Barrier iterations : 11\n", "\n" ] diff --git a/dev/generated/Polynomial Optimization/qp/index.html b/dev/generated/Polynomial Optimization/qp/index.html index 28b0179ea..9ca9cb9f7 100644 --- a/dev/generated/Polynomial Optimization/qp/index.html +++ b/dev/generated/Polynomial Optimization/qp/index.html @@ -71,7 +71,7 @@ 5 1.8390e+10 2.0786e+10 1.30e-01 2.05e-07 2.78e-08 2.40e+09 3.71e-05 9.86e-01 --------------------------------------------------------------------------------------------- Terminated with status = primal infeasible -solve time = 1.52ms +solve time = 1.43ms * Solver : Clarabel * Status @@ -87,7 +87,7 @@ Dual objective value : -2.07856e+10 * Work counters - Solve time (sec) : 1.51995e-03 + Solve time (sec) : 1.43054e-03 Barrier iterations : 5

Indeed, as the constraints have degree 1 and their multipliers are SOS so they have an even degree, with maxdegree 2 we can only use degree 0 multipliers hence constants. The terms of maximal degree in resulting sum will therefore only be in -x' * Q * x/2 hence it is not SOS whatever is the value of the multipliers. Let's try with maxdegree 3 so that the multipliers can be quadratic. This second level is now feasible and gives a lower bound of -22.

model3 = solve(3)
-------------------------------------------------------------
            Clarabel.jl v0.7.1  -  Clever Acronym
                    (c) Paul Goulart
@@ -130,7 +130,7 @@
  11   2.2000e+01   2.2000e+01  3.49e-10  7.90e-11  1.92e-11  8.30e-09  3.83e-09  9.88e-01
 ---------------------------------------------------------------------------------------------
 Terminated with status = solved
-solve time = 16.4ms
+solve time = 16.3ms
 * Solver : Clarabel
 
 * Status
@@ -146,5 +146,5 @@
   Dual objective value : -2.20000e+01
 
 * Work counters
-  Solve time (sec)   : 1.63722e-02
-  Barrier iterations : 11

This page was generated using Literate.jl.

+ Solve time (sec) : 1.63315e-02 + Barrier iterations : 11

This page was generated using Literate.jl.

diff --git a/dev/generated/Sparsity/sign_symmetry.ipynb b/dev/generated/Sparsity/sign_symmetry.ipynb index d41ce6246..8111a140a 100644 --- a/dev/generated/Sparsity/sign_symmetry.ipynb +++ b/dev/generated/Sparsity/sign_symmetry.ipynb @@ -104,7 +104,7 @@ " Dual objective value : 0.00000e+00\n", "\n", "* Work counters\n", - " Solve time (sec) : 4.46081e-04\n", + " Solve time (sec) : 4.47035e-04\n", "\n" ] }, diff --git a/dev/generated/Sparsity/sign_symmetry/index.html b/dev/generated/Sparsity/sign_symmetry/index.html index d89900e06..c95fc7b64 100644 --- a/dev/generated/Sparsity/sign_symmetry/index.html +++ b/dev/generated/Sparsity/sign_symmetry/index.html @@ -23,4 +23,4 @@ monos = [sub.basis.monomials for sub in g.blocks]
3-element Vector{DynamicPolynomials.MonomialVector{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}}}:
  [x₂, x₁]
  [x₃]
- [1, x₂², x₁x₂, x₁²]

This page was generated using Literate.jl.

+ [1, x₂², x₁x₂, x₁²]

This page was generated using Literate.jl.

diff --git a/dev/generated/Sparsity/term_sparsity/index.html b/dev/generated/Sparsity/term_sparsity/index.html index b5d9e50d6..bb120acda 100644 --- a/dev/generated/Sparsity/term_sparsity/index.html +++ b/dev/generated/Sparsity/term_sparsity/index.html @@ -21,4 +21,4 @@ MonomialBasis([x₂, x₁, x₁x₂]) MonomialBasis([x₂, x₂x₃, x₁x₂]) MonomialBasis([x₃, x₂, x₂x₃]) - MonomialBasis([1, x₂x₃, x₁x₂])

This page was generated using Literate.jl.

+ MonomialBasis([1, x₂x₃, x₁x₂])

This page was generated using Literate.jl.

diff --git a/dev/generated/Symmetry/cyclic.ipynb b/dev/generated/Symmetry/cyclic.ipynb index 3409c547b..2c8ef6ed0 100644 --- a/dev/generated/Symmetry/cyclic.ipynb +++ b/dev/generated/Symmetry/cyclic.ipynb @@ -173,7 +173,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.22045e-16\n Dual objective value : -2.20229e-10\n\n* Work counters\n Solve time (sec) : 1.03021e-03\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 2.22045e-16\n Dual objective value : -2.20229e-10\n\n* Work counters\n Solve time (sec) : 1.02305e-03\n" }, "metadata": {}, "execution_count": 4 diff --git a/dev/generated/Symmetry/cyclic/index.html b/dev/generated/Symmetry/cyclic/index.html index a16ebf1d8..01f472d05 100644 --- a/dev/generated/Symmetry/cyclic/index.html +++ b/dev/generated/Symmetry/cyclic/index.html @@ -82,7 +82,7 @@ Dual objective value : -2.20229e-10 * Work counters - Solve time (sec) : 1.01209e-03 + Solve time (sec) : 1.02782e-03

Let's look at the symmetry adapted basis used.

for gram in gram_matrix(con_ref).blocks
     println(gram.basis.polynomials)
     display(gram.Q)
@@ -134,4 +134,4 @@
 DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, ComplexF64}[(1.0 - 0.0im), (-0.5773502691896257 - 0.0im)x₃ + (-0.5773502691896257 - 0.0im)x₂ + (-0.5773502691896257 - 0.0im)x₁]
 DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, ComplexF64}[(-0.577350269189626 - 0.0im)x₃ + (0.2886751345948128 + 0.5000000000000001im)x₂ + (0.28867513459481314 - 0.49999999999999994im)x₁]
 DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, ComplexF64}[(-0.577350269189626 - 0.0im)x₃ + (0.28867513459481314 - 0.49999999999999994im)x₂ + (0.2886751345948128 + 0.5000000000000001im)x₁]

We can see that the real invariant subspace was in fact coming from two complex conjugate complex invariant subspaces:

complex_basis = basis[1] + im * basis[2]
-image = Symmetry.SymbolicWedderburn.action(action, g, complex_basis)

\[ (0.4082482904638631 - 0.7071067811865475im)x_{3} + (0.4082482904638631 + 0.7071067811865475im)x_{2} + (-0.8164965809277261 + 0.0im)x_{1} \]

And there is a direct correspondance between the representation of the real and complex versions:

(a + b * im) * complex_basis

\[ (0.4082482904638631 - 0.7071067811865476im)x_{3} + (0.4082482904638629 + 0.7071067811865475im)x_{2} + (-0.816496580927726 + 5.551115123125783e-17im)x_{1} \]

This page was generated using Literate.jl.

+image = Symmetry.SymbolicWedderburn.action(action, g, complex_basis)

\[ (0.4082482904638631 - 0.7071067811865475im)x_{3} + (0.4082482904638631 + 0.7071067811865475im)x_{2} + (-0.8164965809277261 + 0.0im)x_{1} \]

And there is a direct correspondance between the representation of the real and complex versions:

(a + b * im) * complex_basis

\[ (0.4082482904638631 - 0.7071067811865476im)x_{3} + (0.4082482904638629 + 0.7071067811865475im)x_{2} + (-0.816496580927726 + 5.551115123125783e-17im)x_{1} \]

This page was generated using Literate.jl.

diff --git a/dev/generated/Symmetry/dihedral/index.html b/dev/generated/Symmetry/dihedral/index.html index 471f36a94..cdb92c380 100644 --- a/dev/generated/Symmetry/dihedral/index.html +++ b/dev/generated/Symmetry/dihedral/index.html @@ -146,4 +146,4 @@ DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[-x³, -xy², -x] DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[1.0, -0.7071067811865472y² - 0.7071067811865475x²] DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[xy] -DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[-0.7071067811865472y² + 0.7071067811865475x²]

We notice that we indeed find -3825/4096 and that symmetry was exploited.

This page was generated using Literate.jl.

+DynamicPolynomials.Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, MultivariatePolynomials.Graded{MultivariatePolynomials.LexOrder}, Float64}[-0.7071067811865472y² + 0.7071067811865475x²]

We notice that we indeed find -3825/4096 and that symmetry was exploited.

This page was generated using Literate.jl.

diff --git a/dev/generated/Symmetry/even_reduction/index.html b/dev/generated/Symmetry/even_reduction/index.html index 3f1d3e538..71f9c2917 100644 --- a/dev/generated/Symmetry/even_reduction/index.html +++ b/dev/generated/Symmetry/even_reduction/index.html @@ -32,4 +32,4 @@ [2] Block with row/column basis: FixedPolynomialBasis([x]) And entries in a 1×1 SymMatrix{Float64}: - 4.011410529947057e-9

This page was generated using Literate.jl.

+ 4.011410529947057e-9

This page was generated using Literate.jl.

diff --git a/dev/generated/Symmetry/permutation_symmetry/index.html b/dev/generated/Symmetry/permutation_symmetry/index.html index 02511c9ba..b0a882a98 100644 --- a/dev/generated/Symmetry/permutation_symmetry/index.html +++ b/dev/generated/Symmetry/permutation_symmetry/index.html @@ -31,4 +31,4 @@ GramMatrix with row/column basis: FixedPolynomialBasis([-0.5*x[4] + 0.5*x[3] - 0.5*x[2] + 0.5*x[1]]) And entries in a 1×1 SymMatrix{Float64}: - 0.9999999999999998

This page was generated using Literate.jl.

+ 0.9999999999999998

This page was generated using Literate.jl.

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b/dev/generated/Systems and Control/barrier_certificate/39b865bc.svg similarity index 90% rename from dev/generated/Systems and Control/barrier_certificate/9d6f1f67.svg rename to dev/generated/Systems and Control/barrier_certificate/39b865bc.svg index 5be3ac996..e8663ad70 100644 --- a/dev/generated/Systems and Control/barrier_certificate/9d6f1f67.svg +++ b/dev/generated/Systems and Control/barrier_certificate/39b865bc.svg @@ -1,1400 +1,1400 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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--git a/dev/generated/Systems and Control/barrier_certificate/index.html b/dev/generated/Systems and Control/barrier_certificate/index.html index 78d7de3bf..21e13ef67 100644 --- a/dev/generated/Systems and Control/barrier_certificate/index.html +++ b/dev/generated/Systems and Control/barrier_certificate/index.html @@ -36,4 +36,4 @@ Plots.plot!(xlims = (-2, 3), ylims = (-2.5, 2.5)) end -phase_plot(f, value(B), g₁, h₁, 10, 30.0, [[x1, x2] for x1 in 1.2:0.2:1.7, x2 in -0.35:0.1:0.35])Example block output

This page was generated using Literate.jl.

+phase_plot(f, value(B), g₁, h₁, 10, 30.0, [[x1, x2] for x1 in 1.2:0.2:1.7, x2 in -0.35:0.1:0.35])Example block output

This page was generated using Literate.jl.

diff --git a/dev/generated/Systems and Control/julia_set.ipynb b/dev/generated/Systems and Control/julia_set.ipynb index 9b161770f..42d8ab866 100644 --- a/dev/generated/Systems and Control/julia_set.ipynb +++ b/dev/generated/Systems and Control/julia_set.ipynb @@ -276,7 +276,7 @@ { "output_type": "execute_result", "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 6.02400e+00\n Dual objective value : 6.02400e+00\n\n* Work counters\n Solve time (sec) : 1.41630e-02\n" + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 6.02400e+00\n Dual objective value : 6.02400e+00\n\n* Work counters\n Solve time (sec) : 1.43781e-02\n" }, "metadata": {}, "execution_count": 8 @@ -317,46881 +317,108 @@ "\n", "\n", "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "\n", - " \n", - " \n", - " \n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - 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NEARLY_FEASIBLE_POINT\n Dual status : NEARLY_FEASIBLE_POINT\n Objective value : 5.03023e+00\n Dual objective value : 5.03038e+00\n\n* Work counters\n Solve time (sec) : 4.10248e-01\n" - }, - "metadata": {}, - "execution_count": 10 - } - ], - "cell_type": "code", - "source": [ - "model = outer_approximation(solver, 4, c)\n", - "solution_summary(model)" - ], - "metadata": {}, - "execution_count": 10 - }, - { - "cell_type": "markdown", - "source": [ - "We visualize below:" - ], - "metadata": {} - }, - { - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "┌ Warning: Skipped marker arg pixel.\n", - "└ @ Plots ~/.julia/packages/Plots/ju9dp/src/args.jl:1149\n" - ] - }, - { - "output_type": "execute_result", - "data": { - "text/plain": "Plot{Plots.GRBackend() n=2}", - "image/png": 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- "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - "metadata": {}, - "execution_count": 11 - } - ], - "cell_type": "code", - "source": [ - "julia_plot(value(model[:v]), c)" - ], - "metadata": {}, - "execution_count": 11 - }, - { - "cell_type": "markdown", - "source": [ - "Let's now use the value of `c` corresponding to the right image of [KHJ14, Figure 3] and with degree 2." - ], - "metadata": {} - }, - { - "outputs": [ - { - "output_type": "execute_result", - "data": { - "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 6.57446e+00\n Dual objective value : 6.57446e+00\n\n* Work counters\n Solve time (sec) : 1.51181e-02\n" - }, - "metadata": {}, - "execution_count": 12 - } - ], - "cell_type": "code", - "source": [ - "c = -0.9 + 0.2im\n", - "model = outer_approximation(solver, 2, c)\n", - "solution_summary(model)" - ], - "metadata": {}, - "execution_count": 12 - }, - { - "cell_type": "markdown", - "source": [ - "We visualize below:" - ], - "metadata": {} - }, - { - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "┌ Warning: Skipped marker arg pixel.\n", - "└ @ Plots ~/.julia/packages/Plots/ju9dp/src/args.jl:1149\n" - ] - }, - { - "output_type": "execute_result", - "data": { - "text/plain": "Plot{Plots.GRBackend() n=2}", - "image/png": 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optimality.\"\n\n* Candidate solution (result #1)\n Primal status : NEARLY_FEASIBLE_POINT\n Dual status : NEARLY_FEASIBLE_POINT\n Objective value : 5.03758e+00\n Dual objective value : 5.04107e+00\n\n* Work counters\n Solve time (sec) : 4.01483e-01\n" - }, - "metadata": {}, - "execution_count": 14 - } - ], - "cell_type": "code", - "source": [ - "model = outer_approximation(solver, 4, c)\n", - "solution_summary(model)" - ], - "metadata": {}, - "execution_count": 14 - }, - { - "cell_type": "markdown", - "source": [ - "We visualize below:" - ], - "metadata": {} - }, - { - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "┌ Warning: Skipped marker arg pixel.\n", - "└ @ Plots ~/.julia/packages/Plots/ju9dp/src/args.jl:1149\n" - ] - }, - { - "output_type": "execute_result", - "data": { - "text/plain": "Plot{Plots.GRBackend() n=2}", - "image/png": 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"\n", "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", @@ -47199,9 +426,13 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47210,10 +441,13 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -47222,11 +456,15 @@ "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", "\n", "\n", "\n", @@ -47235,7 +473,17 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -47247,6 +495,17 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47257,6 +516,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47264,60 +533,167 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47325,7 +701,27 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47334,6 +730,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47343,6 +758,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47353,6 +783,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47365,6 +810,24 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47375,8 +838,18 @@ "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47392,14 +865,21 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -47414,17 +894,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -47446,15 +935,29 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -47477,13 +980,27 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47506,17 +1023,25 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -47541,13 +1066,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -47574,15 +1111,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", - "\n", "\n", - "\n", "\n", "\n", "\n", @@ -47610,8 +1158,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47647,8 +1208,27 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47684,9 +1264,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47717,10 +1319,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47752,8 +1375,29 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47785,7 +1429,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47815,6 +1482,33 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47841,6 +1535,32 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47867,7 +1587,23 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47893,8 +1629,24 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47920,6 +1672,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47940,8 +1707,23 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -47960,7 +1742,25 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47976,6 +1776,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -47992,7 +1812,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48008,8 +1851,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48021,9 +1891,38 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48034,9 +1933,39 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48048,6 +1977,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48059,6 +2021,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48068,6 +2066,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48078,6 +2116,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48088,13 +2165,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48105,6 +2214,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48115,8 +2227,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48125,6 +2259,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48135,10 +2272,33 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48147,7 +2307,12 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48158,7 +2323,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48169,7 +2358,12 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48179,7 +2373,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48189,6 +2411,10 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48199,8 +2425,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48209,6 +2462,11 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48221,8 +2479,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48235,7 +2531,48 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48249,6 +2586,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48262,6 +2636,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48275,10 +2688,49 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48293,10 +2745,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48312,10 +2802,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48331,8 +2859,50 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48348,8 +2918,45 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48370,6 +2977,40 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48391,7 +3032,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48415,7 +3088,36 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48440,6 +3142,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48464,10 +3203,42 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48492,13 +3263,37 @@ "\n", "\n", "\n", + "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48532,11 +3327,43 @@ "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48569,17 +3396,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48611,15 +3467,36 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", - "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48628,6 +3505,7 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -48659,15 +3537,27 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -48715,20 +3605,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48773,22 +3668,28 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", - "\n", "\n", "\n", "\n", @@ -48832,16 +3733,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", @@ -48891,12 +3807,37 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -48945,15 +3886,47 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -49000,6 +3973,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49007,7 +4020,6 @@ "\n", "\n", "\n", - "\n", "\n", "\n", "\n", @@ -49053,7 +4065,16 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49062,6 +4083,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49120,6 +4165,13 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49128,6 +4180,28 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49188,6 +4262,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49198,7 +4278,22 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -49260,15 +4355,44 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -49331,8 +4455,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49340,9 +4472,27 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49408,14 +4558,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49484,14 +4668,44 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49566,14 +4780,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49647,12 +4889,40 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49726,14 +4996,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49808,14 +5106,44 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -49884,14 +5212,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -49957,9 +5319,27 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -49967,8 +5347,16 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50031,15 +5419,44 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50101,7 +5518,22 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50112,6 +5544,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50172,6 +5610,28 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50180,6 +5640,13 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50238,6 +5705,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50246,7 +5737,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50292,7 +5792,6 @@ "\n", "\n", "\n", - "\n", "\n", "\n", "\n", @@ -50300,6 +5799,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50346,15 +5885,47 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", - "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50403,12 +5974,37 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50458,16 +6054,31 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50511,22 +6122,28 @@ "\n", "\n", "\n", - "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50571,20 +6188,25 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50632,15 +6254,27 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -50672,6 +6306,7 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -50680,15 +6315,36 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50720,17 +6376,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50763,11 +6448,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50801,13 +6518,37 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -50832,10 +6573,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50860,6 +6633,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50884,7 +6694,36 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50908,7 +6747,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50930,6 +6801,40 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50950,8 +6855,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50967,8 +6909,50 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -50984,10 +6968,48 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51003,10 +7025,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51021,10 +7081,49 @@ "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51038,6 +7137,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51051,6 +7189,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51064,7 +7239,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51077,8 +7293,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51091,6 +7345,11 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51099,8 +7358,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51111,6 +7397,10 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51120,7 +7410,35 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51130,7 +7448,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51141,7 +7464,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51152,7 +7499,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51161,10 +7513,33 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51175,6 +7550,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51183,8 +7561,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51195,6 +7595,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51205,13 +7608,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51222,6 +7657,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51232,6 +7706,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51241,6 +7755,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51252,6 +7802,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51263,9 +7846,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51276,9 +7889,38 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51290,8 +7932,35 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51307,7 +7976,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51324,6 +8016,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51339,7 +8051,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51358,8 +8088,23 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51380,6 +8125,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51405,8 +8165,24 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51432,7 +8208,23 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51459,6 +8251,32 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51485,6 +8303,33 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51514,7 +8359,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51546,8 +8414,29 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51579,10 +8468,31 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51613,9 +8523,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51651,8 +8583,27 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51688,8 +8639,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51717,15 +8681,26 @@ "\n", "\n", "\n", - "\n", "\n", - "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51752,13 +8727,25 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51783,17 +8770,25 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51816,13 +8811,27 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51845,15 +8854,29 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51875,17 +8898,26 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51900,14 +8932,21 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51923,8 +8962,18 @@ "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51935,6 +8984,24 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51947,6 +9014,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51957,6 +9039,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51966,6 +9063,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -51974,7 +9090,27 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -51982,60 +9118,167 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52043,6 +9286,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52053,6 +9306,17 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52064,7 +9328,17 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52073,11 +9347,15 @@ "\n", "\n", "\n", - "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52086,10 +9364,13 @@ "\n", "\n", "\n", - "\n", - "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52098,9 +9379,13 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52108,35 +9393,65 @@ "\n", "\n", "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", + "\n", "\n", - "\n", + "\n", + "\n", "\n" ], "image/svg+xml": [ @@ -52159,66 +9474,92 @@ " \n", " \n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", @@ -52226,9 +9567,13 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52237,10 +9582,13 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -52249,11 +9597,15 @@ "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", "\n", "\n", "\n", @@ -52262,7 +9614,17 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -52274,6 +9636,17 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52284,6 +9657,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52291,60 +9674,167 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52352,7 +9842,27 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52361,6 +9871,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52370,6 +9899,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52380,6 +9924,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52392,6 +9951,24 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52402,8 +9979,18 @@ "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52419,14 +10006,21 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -52441,17 +10035,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -52473,15 +10076,29 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -52504,13 +10121,27 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52533,17 +10164,25 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -52568,13 +10207,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -52601,15 +10252,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", - "\n", "\n", - "\n", "\n", "\n", "\n", @@ -52637,8 +10299,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52674,8 +10349,27 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52711,9 +10405,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52744,10 +10460,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52779,8 +10516,29 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52812,7 +10570,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52842,6 +10623,33 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52868,6 +10676,32 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52894,7 +10728,23 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52920,8 +10770,24 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52947,6 +10813,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -52967,8 +10848,23 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -52987,7 +10883,25 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53003,6 +10917,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53019,7 +10953,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53035,8 +10992,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53048,9 +11032,38 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53061,9 +11074,39 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53075,6 +11118,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53086,6 +11162,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53095,6 +11207,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53105,6 +11257,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53115,13 +11306,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53132,6 +11355,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53142,8 +11368,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53152,6 +11400,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53162,10 +11413,33 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53174,7 +11448,12 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53185,7 +11464,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53196,7 +11499,12 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53206,7 +11514,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53216,6 +11552,10 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53226,8 +11566,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53236,6 +11603,11 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53248,8 +11620,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53262,7 +11672,48 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53276,6 +11727,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53289,6 +11777,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53302,10 +11829,49 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53320,10 +11886,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53339,10 +11943,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53358,8 +12000,50 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53375,8 +12059,45 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53397,6 +12118,40 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53418,7 +12173,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53442,7 +12229,36 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53467,6 +12283,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53491,10 +12344,42 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53519,13 +12404,37 @@ "\n", "\n", "\n", + "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53559,11 +12468,43 @@ "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53596,17 +12537,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53638,15 +12608,36 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", - "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53655,6 +12646,7 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -53686,15 +12678,27 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -53742,20 +12746,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53800,22 +12809,28 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", - "\n", "\n", "\n", "\n", @@ -53859,16 +12874,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", @@ -53918,12 +12948,37 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -53972,15 +13027,47 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", @@ -54027,6 +13114,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54034,7 +13161,6 @@ "\n", "\n", "\n", - "\n", "\n", "\n", "\n", @@ -54080,7 +13206,16 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54089,6 +13224,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54147,6 +13306,13 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54155,6 +13321,28 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54215,6 +13403,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54225,7 +13419,22 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -54287,15 +13496,44 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -54358,8 +13596,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54367,9 +13613,27 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54435,14 +13699,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54511,14 +13809,44 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54593,14 +13921,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54674,12 +14030,40 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54753,14 +14137,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54835,14 +14247,44 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -54911,14 +14353,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -54984,9 +14460,27 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -54994,8 +14488,16 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55058,15 +14560,44 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55128,7 +14659,22 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55139,6 +14685,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55199,6 +14751,28 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55207,6 +14781,13 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55265,6 +14846,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55273,7 +14878,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55319,7 +14933,6 @@ "\n", "\n", "\n", - "\n", "\n", "\n", "\n", @@ -55327,6 +14940,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55373,15 +15026,47 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", - "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55430,12 +15115,37 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55485,16 +15195,31 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55538,22 +15263,28 @@ "\n", "\n", "\n", - "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55598,20 +15329,25 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55659,15 +15395,27 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -55699,6 +15447,7 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -55707,15 +15456,36 @@ "\n", "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55747,17 +15517,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55790,11 +15589,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55828,13 +15659,37 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -55859,10 +15714,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55887,6 +15774,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55911,7 +15835,36 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55935,7 +15888,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55957,6 +15942,40 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55977,8 +15996,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -55994,8 +16050,50 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56011,10 +16109,48 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56030,10 +16166,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56048,10 +16222,49 @@ "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56065,6 +16278,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56078,6 +16330,43 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56091,7 +16380,48 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56104,8 +16434,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56118,6 +16486,11 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56126,8 +16499,35 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56138,6 +16538,10 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56147,7 +16551,35 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56157,7 +16589,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56168,7 +16605,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56179,7 +16640,12 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56188,10 +16654,33 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56202,6 +16691,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56210,8 +16702,30 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56222,6 +16736,9 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56232,13 +16749,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56249,6 +16798,45 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56259,6 +16847,46 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56268,6 +16896,42 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56279,6 +16943,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56290,9 +16987,39 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56303,9 +17030,38 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56317,8 +17073,35 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56334,7 +17117,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56351,6 +17157,26 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56366,7 +17192,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56385,8 +17229,23 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56407,6 +17266,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56432,8 +17306,24 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56459,7 +17349,23 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56486,6 +17392,32 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56512,6 +17444,33 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56541,7 +17500,30 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56573,8 +17555,29 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56606,10 +17609,31 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56640,9 +17664,31 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56678,8 +17724,27 @@ "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56715,8 +17780,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56744,15 +17822,26 @@ "\n", "\n", "\n", - "\n", "\n", - "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56779,13 +17868,25 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56810,17 +17911,25 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", "\n", @@ -56843,13 +17952,27 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56872,15 +17995,29 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56902,17 +18039,26 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56927,14 +18073,21 @@ "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56950,8 +18103,18 @@ "\n", "\n", "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56962,6 +18125,24 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56974,6 +18155,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56984,6 +18180,21 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -56993,6 +18204,25 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57001,7 +18231,27 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", @@ -57009,60 +18259,167 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57070,6 +18427,16 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57080,6 +18447,17 @@ "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57091,7 +18469,17 @@ "\n", "\n", "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57100,11 +18488,15 @@ "\n", "\n", "\n", - "\n", "\n", "\n", "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57113,10 +18505,13 @@ "\n", "\n", "\n", - "\n", - "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57125,9 +18520,13 @@ "\n", "\n", "\n", - "\n", - "\n", - "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", @@ -57135,35 +18534,38636 @@ "\n", "\n", "\n", - "\n", - "\n", + "\n", "\n", "\n", "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", + "\n", + "\n", + "\n", + "\n", "\n", "\n", "\n", + "\n", + "\n", "\n", "\n", "\n", - "\n", + "\n", "\n", - "\n", + "\n", + "\n", + "\n" + ] + }, + "metadata": {}, + "execution_count": 9 + } + ], + "cell_type": "code", + "source": [ + "julia_plot(value(model[:v]), c)" + ], + "metadata": {}, + "execution_count": 9 + }, + { + "cell_type": "markdown", + "source": [ + "Let's now look at degree 4." + ], + "metadata": {} + }, + { + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : ALMOST_OPTIMAL\n Message from the solver:\n \"Problem solved to near optimality.\"\n\n* Candidate solution (result #1)\n Primal status : NEARLY_FEASIBLE_POINT\n Dual status : NEARLY_FEASIBLE_POINT\n Objective value : 5.03023e+00\n Dual objective value : 5.03038e+00\n\n* Work counters\n Solve time (sec) : 3.56493e-01\n" + }, + "metadata": {}, + "execution_count": 10 + } + ], + "cell_type": "code", + "source": [ + "model = outer_approximation(solver, 4, c)\n", + "solution_summary(model)" + ], + "metadata": {}, + "execution_count": 10 + }, + { + "cell_type": "markdown", + "source": [ + "We visualize below:" + ], + "metadata": {} + }, + { + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "┌ Warning: Skipped marker arg pixel.\n", + "└ @ Plots ~/.julia/packages/Plots/ju9dp/src/args.jl:1149\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": "Plot{Plots.GRBackend() n=2}", + "image/png": 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+ "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + "metadata": {}, + "execution_count": 11 + } + ], + "cell_type": "code", + "source": [ + "julia_plot(value(model[:v]), c)" + ], + "metadata": {}, + "execution_count": 11 + }, + { + "cell_type": "markdown", + "source": [ + "Let's now use the value of `c` corresponding to the right image of [KHJ14, Figure 3] and with degree 2." + ], + "metadata": {} + }, + { + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 6.57446e+00\n Dual objective value : 6.57446e+00\n\n* Work counters\n Solve time (sec) : 1.49491e-02\n" + }, + "metadata": {}, + "execution_count": 12 + } + ], + "cell_type": "code", + "source": [ + "c = -0.9 + 0.2im\n", + "model = outer_approximation(solver, 2, c)\n", + "solution_summary(model)" + ], + "metadata": {}, + "execution_count": 12 + }, + { + "cell_type": "markdown", + "source": [ + "We visualize below:" + ], + "metadata": {} + }, + { + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "┌ Warning: Skipped marker arg pixel.\n", + "└ @ Plots ~/.julia/packages/Plots/ju9dp/src/args.jl:1149\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": "Plot{Plots.GRBackend() n=2}", + "image/png": 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Candidate solution (result #1)\n Primal status : NEARLY_FEASIBLE_POINT\n Dual status : NEARLY_FEASIBLE_POINT\n Objective value : 5.03758e+00\n Dual objective value : 5.04107e+00\n\n* Work counters\n Solve time (sec) : 3.90406e-01\n" + }, + "metadata": {}, + "execution_count": 14 + } + ], + "cell_type": "code", + "source": [ + "model = outer_approximation(solver, 4, c)\n", + "solution_summary(model)" + ], + "metadata": {}, + "execution_count": 14 + }, + { + "cell_type": "markdown", + "source": [ + "We visualize below:" + ], + "metadata": {} + }, + { + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "┌ Warning: Skipped marker arg pixel.\n", + "└ @ Plots ~/.julia/packages/Plots/ju9dp/src/args.jl:1149\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": "Plot{Plots.GRBackend() n=2}", + "image/png": 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + diff --git a/dev/generated/Systems and Control/julia_set/index.html b/dev/generated/Systems and Control/julia_set/index.html index 950227a81..d0d10e66b 100644 --- a/dev/generated/Systems and Control/julia_set/index.html +++ b/dev/generated/Systems and Control/julia_set/index.html @@ -83,8 +83,8 @@ Dual objective value : 6.02400e+00 * Work counters - Solve time (sec) : 1.41830e-02 -

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

Let's now look at degree 4.

model = outer_approximation(solver, 4, c)
+  Solve time (sec)   : 1.42729e-02
+

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

Let's now look at degree 4.

model = outer_approximation(solver, 4, c)
 solution_summary(model)
* Solver : CSDP
 
 * Status
@@ -100,8 +100,8 @@
   Dual objective value : 5.03038e+00
 
 * Work counters
-  Solve time (sec)   : 3.74798e-01
-

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

Let's now use the value of c corresponding to the right image of [KHJ14, Figure 3] and with degree 2.

c = -0.9 + 0.2im
+  Solve time (sec)   : 4.09037e-01
+

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

Let's now use the value of c corresponding to the right image of [KHJ14, Figure 3] and with degree 2.

c = -0.9 + 0.2im
 model = outer_approximation(solver, 2, c)
 solution_summary(model)
* Solver : CSDP
 
@@ -118,8 +118,8 @@
   Dual objective value : 6.57446e+00
 
 * Work counters
-  Solve time (sec)   : 1.49312e-02
-

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

Let's now look at degree 4.

model = outer_approximation(solver, 4, c)
+  Solve time (sec)   : 1.70021e-02
+

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

Let's now look at degree 4.

model = outer_approximation(solver, 4, c)
 solution_summary(model)
* Solver : CSDP
 
 * Status
@@ -135,5 +135,5 @@
   Dual objective value : 5.04107e+00
 
 * Work counters
-  Solve time (sec)   : 4.08291e-01
-

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

This page was generated using Literate.jl.

+ Solve time (sec) : 3.97363e-01 +

We visualize below:

julia_plot(value(model[:v]), c)
Example block output

This page was generated using Literate.jl.

diff --git a/dev/generated/Systems and Control/lyapunov_function_search/index.html b/dev/generated/Systems and Control/lyapunov_function_search/index.html index 7c24c6f9f..b89143429 100644 --- a/dev/generated/Systems and Control/lyapunov_function_search/index.html +++ b/dev/generated/Systems and Control/lyapunov_function_search/index.html @@ -12,4 +12,4 @@ x₁² x₂² x₃²

We now define the Lyapunov function as a polynomial decision variable with these monomials:

@variable(model, V, Poly(monos))

\[ ({\_}_{1})x_{3}^{2} + ({\_}_{2})x_{2}^{2} + ({\_}_{3})x_{1}^{2} \]

We need to make sure that the Lyapunov function is strictly positive. We can do this with a constraint $V(x) \ge \epsilon (x_1^2 + x_2^2 + x_3^2)$, let's pick $\epsilon = 1$:

@constraint(model, V >= sum(x.^2))

\[ ({\_}_{1} - 1)x_{3}^{2} + ({\_}_{2} - 1)x_{2}^{2} + ({\_}_{3} - 1)x_{1}^{2} \text{ is SOS} \]

We now compute $\text{d}V/\text{d}x \cdot f$.

using LinearAlgebra # Needed for `dot`
-dVdt = dot(differentiate(V, x), f)

\[ \frac{(-8 {\_}_{1})x_{3}^{2} + (-2 {\_}_{2})x_{2}^{2} + (-2 {\_}_{1})x_{3}^{4} + (-2 {\_}_{2})x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{2} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2} + (-2 {\_}_{3})x_{1}^{4} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{4} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3})x_{1}^{4}x_{3}^{2}}{1 + x_{3}^{2}} \]

The denominator is $x[3]^2 + 1$ is strictly positive so the sign of dVdt is the same as the sign of its numerator.

P = dVdt.num

\[ (-8 {\_}_{1})x_{3}^{2} + (-2 {\_}_{2})x_{2}^{2} + (-2 {\_}_{1})x_{3}^{4} + (-2 {\_}_{2})x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{2} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2} + (-2 {\_}_{3})x_{1}^{4} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{4} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3})x_{1}^{4}x_{3}^{2} \]

Hence, we constrain this numerator to be nonnegative:

@constraint(model, P <= 0)

\[ (8 {\_}_{1})x_{3}^{2} + (2 {\_}_{2})x_{2}^{2} + (2 {\_}_{1})x_{3}^{4} + (2 {\_}_{2})x_{2}^{2}x_{3}^{2} + (-6 {\_}_{1} + 2 {\_}_{3})x_{1}^{2}x_{3}^{2} + (2 {\_}_{2})x_{1}^{2}x_{2}^{2} + (2 {\_}_{3})x_{1}^{4} + (-6 {\_}_{1} + 2 {\_}_{3})x_{1}^{2}x_{3}^{4} + (2 {\_}_{2})x_{1}^{2}x_{2}^{2}x_{3}^{2} + (2 {\_}_{3})x_{1}^{4}x_{3}^{2} \text{ is SOS} \]

The model is ready to be optimized by the solver:

JuMP.optimize!(model)

We verify that the solver has found a feasible solution:

JuMP.primal_status(model)
FEASIBLE_POINT::ResultStatusCode = 1

We can now obtain this feasible solution with:

value(V)

\[ 2.9958453255028186x_{3}^{2} + 12.286107321105156x_{2}^{2} + 15.718362431619155x_{1}^{2} \]

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+dVdt = dot(differentiate(V, x), f)

\[ \frac{(-8 {\_}_{1})x_{3}^{2} + (-2 {\_}_{2})x_{2}^{2} + (-2 {\_}_{1})x_{3}^{4} + (-2 {\_}_{2})x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{2} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2} + (-2 {\_}_{3})x_{1}^{4} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{4} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3})x_{1}^{4}x_{3}^{2}}{1 + x_{3}^{2}} \]

The denominator is $x[3]^2 + 1$ is strictly positive so the sign of dVdt is the same as the sign of its numerator.

P = dVdt.num

\[ (-8 {\_}_{1})x_{3}^{2} + (-2 {\_}_{2})x_{2}^{2} + (-2 {\_}_{1})x_{3}^{4} + (-2 {\_}_{2})x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{2} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2} + (-2 {\_}_{3})x_{1}^{4} + (-2 {\_}_{3} + 6 {\_}_{1})x_{1}^{2}x_{3}^{4} + (-2 {\_}_{2})x_{1}^{2}x_{2}^{2}x_{3}^{2} + (-2 {\_}_{3})x_{1}^{4}x_{3}^{2} \]

Hence, we constrain this numerator to be nonnegative:

@constraint(model, P <= 0)

\[ (8 {\_}_{1})x_{3}^{2} + (2 {\_}_{2})x_{2}^{2} + (2 {\_}_{1})x_{3}^{4} + (2 {\_}_{2})x_{2}^{2}x_{3}^{2} + (-6 {\_}_{1} + 2 {\_}_{3})x_{1}^{2}x_{3}^{2} + (2 {\_}_{2})x_{1}^{2}x_{2}^{2} + (2 {\_}_{3})x_{1}^{4} + (-6 {\_}_{1} + 2 {\_}_{3})x_{1}^{2}x_{3}^{4} + (2 {\_}_{2})x_{1}^{2}x_{2}^{2}x_{3}^{2} + (2 {\_}_{3})x_{1}^{4}x_{3}^{2} \text{ is SOS} \]

The model is ready to be optimized by the solver:

JuMP.optimize!(model)

We verify that the solver has found a feasible solution:

JuMP.primal_status(model)
FEASIBLE_POINT::ResultStatusCode = 1

We can now obtain this feasible solution with:

value(V)

\[ 2.9958453255028186x_{3}^{2} + 12.286107321105156x_{2}^{2} + 15.718362431619155x_{1}^{2} \]

This page was generated using Literate.jl.

diff --git a/dev/generated/Systems and Control/stabilization_of_nonlinear_systems.ipynb b/dev/generated/Systems and Control/stabilization_of_nonlinear_systems.ipynb index 5edb435e2..2b874ec36 100644 --- a/dev/generated/Systems and Control/stabilization_of_nonlinear_systems.ipynb +++ b/dev/generated/Systems and Control/stabilization_of_nonlinear_systems.ipynb @@ -136,2750 +136,2750 @@ "\n", "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", + "\n", "\n", - " \n", + " \n", " \n", " \n", "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "\n", - 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Control/stabilization_of_nonlinear_systems/e258f0dc.svg @@ -1,1375 +1,1375 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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Control/stabilization_of_nonlinear_systems/f1ce61b0.svg +++ b/dev/generated/Systems and Control/stabilization_of_nonlinear_systems/f29923b0.svg @@ -1,1367 +1,1367 @@ - + - + - + - + - + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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phase_plot (generic function with 2 methods)

Example 1

g = [0, 1]
 f = [x[2] - x[1]^3 + x[1]^2, 0]
 b = 3x[1]^2 + 2x[1]*x[2] + 2x[2]^2
-u = controller(f, g, b, 4, 0:3)

\[ -0.5738994625385273x_{2} - 1.2298305281744644x_{1} - 0.12930340072544455x_{2}^{3} \]

We find the controller above which gives the following phase plot.

phase_plot(f + g * u, 200, 10.0, [[x1, x2] for x1 in -5:5:5, x2 in -5:5:5 if x1 != 0 || x2 != 0])
Example block output

Example 2

g = [0, 1]
+u = controller(f, g, b, 4, 0:3)

\[ -0.5738994625385273x_{2} - 1.2298305281744644x_{1} - 0.12930340072544455x_{2}^{3} \]

We find the controller above which gives the following phase plot.

phase_plot(f + g * u, 200, 10.0, [[x1, x2] for x1 in -5:5:5, x2 in -5:5:5 if x1 != 0 || x2 != 0])
Example block output

Example 2

g = [0, 1]
 f = [2x[1]^3 + x[1]^2*x[2] - 6x[1]*x[2]^2 + 5x[2]^3, 0]
 b = x[1]^2 + x[2]^2
-u = controller(f, g, b, 2.5, 0:3)

\[ -3.470949347992857x_{2}^{3} - 6.465434558023581x_{1}x_{2}^{2} + 4.004075892877742x_{1}^{2}x_{2} - 3.1387619181637865x_{1}^{3} \]

We find the controller above which gives the following phase plot.

phase_plot(f + g * u, 2000, 5.0, [[-1.0, -5.0], [1.0, 5.0]])
Example block output

Example 3

g = [0, x[2]]
+u = controller(f, g, b, 2.5, 0:3)

\[ -3.470949347992857x_{2}^{3} - 6.465434558023581x_{1}x_{2}^{2} + 4.004075892877742x_{1}^{2}x_{2} - 3.1387619181637865x_{1}^{3} \]

We find the controller above which gives the following phase plot.

phase_plot(f + g * u, 2000, 5.0, [[-1.0, -5.0], [1.0, 5.0]])
Example block output

Example 3

g = [0, x[2]]
 f = [-6x[1]*x[2]^2 - x[1]^2*x[2] + 2x[2]^3, 0]
 b = x[1]^2 + x[2]^2
 u = controller(f, g, b, 3, 0:2)

\[ -2.737433441558844x_{2}^{2} + 0.18059594494782605x_{1}^{2} \]

We find the controller above which gives the following phase plot.

X0 = [Float64[x1, x2] for x1 in -5:5:5, x2 in -5:5:5 if x2 != 0]
@@ -58,4 +58,4 @@
 push!(X0, [-3, -ε])
 push!(X0, [ 3,  ε])
 push!(X0, [ 4, -ε])
-phase_plot(f + g * u, 2000, 10.0, X0)
Example block output

This page was generated using Literate.jl.

+phase_plot(f + g * u, 2000, 10.0, X0)Example block output

This page was generated using Literate.jl.

diff --git a/dev/index.html b/dev/index.html index 4af6edbc7..e62db2a03 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Index · SumOfSquares
GitHub

SumOfSquares –- Sum of Squares Programming for Julia

SumOfSquares implements Sum of Squares reformulation for PolyJuMP, enabling the creation of sum of squares variables and constraints in JuMP.

The polynomial can be represented by any library implementing the MultivariatePolynomial.jl interface. That is, you can currently choose between DynamicPolynomials and TypedPolynomials. As a rule of thumb, if you know at compile time (or at the time you are writing your code), the number of variable and that this number is small, use TypedPolynomials, otherwise, use DynamicPolynomials.

Contents

+Index · SumOfSquares
GitHub

SumOfSquares –- Sum of Squares Programming for Julia

SumOfSquares implements Sum of Squares reformulation for PolyJuMP, enabling the creation of sum of squares variables and constraints in JuMP.

The polynomial can be represented by any library implementing the MultivariatePolynomial.jl interface. That is, you can currently choose between DynamicPolynomials and TypedPolynomials. As a rule of thumb, if you know at compile time (or at the time you are writing your code), the number of variable and that this number is small, use TypedPolynomials, otherwise, use DynamicPolynomials.

Contents

diff --git a/dev/sumofsquares/index.html b/dev/sumofsquares/index.html index b642cfe42..d0d94a3dd 100644 --- a/dev/sumofsquares/index.html +++ b/dev/sumofsquares/index.html @@ -1,2 +1,2 @@ -Sum-of-Squares Programming · SumOfSquares
GitHub

Sum-of-Squares Programming

This section contains a brief introduction to Sum-of-Squares Programming. For more details, see [BPT12, Las09, Lau09].

Quadratic forms and Semidefinite programming

The positive semidefiniteness of a $n \times n$ real symmetric matrix $Q$ is equivalent to the nonnegativity of the quadratic form $p(x) = x^\top Q x$ for all vector $x \in \mathbb{R}^n$. For instance, the polynomial

\[x_1^2 + 2x_1x_2 + 5x_2^2 + 4x_2x_3 + x_3^2 = x^\top \begin{pmatrix}1 & 1 & 0\\1 & 5 & 2\\ 0 & 2 & 1\end{pmatrix} x\]

is nonnegative since the matrix of the right-hand side is positive semidefinite. Moreover, a certificate of nonnegativity can be extracted from the Cholesky decomposition of the matrix:

\[(x_1 + x_2)^2 + (2x_2 + x_3)^2 = x^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix}^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix} x\]

Polynomial nonnegativity and Semidefinite programming

This can be generalized to a polynomial of arbitrary degree. A polynomial $p(x)$ is nonnegative if it can be rewritten as $p(x) = X^\top Q X$ where $Q$ is a real symmetric positive semidefinite matrix and $X$ is a vector of monomials.

For instance

\[x_1^2 + 2x_1^2x_2 + 5x_1^2x_2^2 + 4x_1x_2^2 + x_2^2 = X^\top \begin{pmatrix}1 & 1 & 0\\1 & 5 & 2\\ 0 & 2 & 1\end{pmatrix} X\]

where $X = (x_1, x_1x_2, x_2)$ Similarly to the previous section, the Cholesky factorization of the matrix can be used to extract a sum of squares certificate of nonnegativity for the polynomial:

\[(x_1 + x_1x_2)^2 + (2x_1x_2 + x_2)^2 = X^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix}^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix} X\]

When is nonnegativity equivalent to sum of squares ?

Determining whether a polynomial is nonnegative is NP-hard. The condition of the previous section was only sufficient, that is, there exists nonnegative polynomials that are not sums of squares. Hilbert showed in 1888 that there are exactly 3 cases for which there is equivalence between the nonnegativity of the polynomials of $n$ variables and degree $2d$ and the existence of a sum of squares decomposition.

  • $n = 1$ : Univariate polynomials
  • $2d = 2$ : Quadratic polynomials
  • $n = 2$, $2d = 4$ : Bivariate quartics

The first explicit example of polynomial that was not a sum of squares was given by Motzkin in 1967:

\[x_1^4x_2^2 + x_1^2x_2^4 + 1 - 3x_1^2x_2^2 \geq 0 \quad \forall x\]

While it is not a sum of squares, it can still be certified to be nonnegative using sum-of-squares programming by identifying it with a rational sum-of-squares decomposition. These facts can be verified numerically using this package as detailed in the Motzkin example.

References

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

[Lau09] Laurent, M. Sums of squares, moment matrices and optimization over polynomials Emerging applications of algebraic geometry, Springer, 2009, 157-270.

+Sum-of-Squares Programming · SumOfSquares
GitHub

Sum-of-Squares Programming

This section contains a brief introduction to Sum-of-Squares Programming. For more details, see [BPT12, Las09, Lau09].

Quadratic forms and Semidefinite programming

The positive semidefiniteness of a $n \times n$ real symmetric matrix $Q$ is equivalent to the nonnegativity of the quadratic form $p(x) = x^\top Q x$ for all vector $x \in \mathbb{R}^n$. For instance, the polynomial

\[x_1^2 + 2x_1x_2 + 5x_2^2 + 4x_2x_3 + x_3^2 = x^\top \begin{pmatrix}1 & 1 & 0\\1 & 5 & 2\\ 0 & 2 & 1\end{pmatrix} x\]

is nonnegative since the matrix of the right-hand side is positive semidefinite. Moreover, a certificate of nonnegativity can be extracted from the Cholesky decomposition of the matrix:

\[(x_1 + x_2)^2 + (2x_2 + x_3)^2 = x^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix}^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix} x\]

Polynomial nonnegativity and Semidefinite programming

This can be generalized to a polynomial of arbitrary degree. A polynomial $p(x)$ is nonnegative if it can be rewritten as $p(x) = X^\top Q X$ where $Q$ is a real symmetric positive semidefinite matrix and $X$ is a vector of monomials.

For instance

\[x_1^2 + 2x_1^2x_2 + 5x_1^2x_2^2 + 4x_1x_2^2 + x_2^2 = X^\top \begin{pmatrix}1 & 1 & 0\\1 & 5 & 2\\ 0 & 2 & 1\end{pmatrix} X\]

where $X = (x_1, x_1x_2, x_2)$ Similarly to the previous section, the Cholesky factorization of the matrix can be used to extract a sum of squares certificate of nonnegativity for the polynomial:

\[(x_1 + x_1x_2)^2 + (2x_1x_2 + x_2)^2 = X^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix}^\top \begin{pmatrix}1 & 1 & 0\\0 & 2 & 1\end{pmatrix} X\]

When is nonnegativity equivalent to sum of squares ?

Determining whether a polynomial is nonnegative is NP-hard. The condition of the previous section was only sufficient, that is, there exists nonnegative polynomials that are not sums of squares. Hilbert showed in 1888 that there are exactly 3 cases for which there is equivalence between the nonnegativity of the polynomials of $n$ variables and degree $2d$ and the existence of a sum of squares decomposition.

  • $n = 1$ : Univariate polynomials
  • $2d = 2$ : Quadratic polynomials
  • $n = 2$, $2d = 4$ : Bivariate quartics

The first explicit example of polynomial that was not a sum of squares was given by Motzkin in 1967:

\[x_1^4x_2^2 + x_1^2x_2^4 + 1 - 3x_1^2x_2^2 \geq 0 \quad \forall x\]

While it is not a sum of squares, it can still be certified to be nonnegative using sum-of-squares programming by identifying it with a rational sum-of-squares decomposition. These facts can be verified numerically using this package as detailed in the Motzkin example.

References

[BPT12] Blekherman, G.; Parrilo, P. A. & Thomas, R. R. Semidefinite Optimization and Convex Algebraic Geometry. Society for Industrial and Applied Mathematics, 2012.

[Lau09] Laurent, M. Sums of squares, moment matrices and optimization over polynomials Emerging applications of algebraic geometry, Springer, 2009, 157-270.

diff --git a/dev/variables/index.html b/dev/variables/index.html index 85a38b784..dbaf0f7fc 100644 --- a/dev/variables/index.html +++ b/dev/variables/index.html @@ -93,4 +93,4 @@ variables::Vector{Vector{MOI.VariableIndex}} constraints::Vector{MOI.ConstraintIndex{ MOI.VectorOfVariables, SOS.PositiveSemidefinite2x2ConeTriangle}} -end

A matrix is SDD iff it is the sum of psd matrices Mij that are zero except for entries ii, ij and jj [Lemma 9, AM17]. This bridge substitute the constrained variables in SOS.ScaledDiagonallyDominantConeTriangle into a sum of constrained variables in SOS.PositiveSemidefinite2x2ConeTriangle.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source +end

A matrix is SDD iff it is the sum of psd matrices Mij that are zero except for entries ii, ij and jj [Lemma 9, AM17]. This bridge substitute the constrained variables in SOS.ScaledDiagonallyDominantConeTriangle into a sum of constrained variables in SOS.PositiveSemidefinite2x2ConeTriangle.

[AM17] Ahmadi, A. A. & Majumdar, A. DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization ArXiv e-prints, 2017.

source