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mode 100644 v0.8.0/search_index.js create mode 100644 v0.8.0/siteinfo.js create mode 100644 v0.8.0/user_guide_c_cpp/index.html create mode 100644 v0.8.0/user_guide_chordal/index.html create mode 100644 v0.8.0/user_guide_r/index.html diff --git a/v0.8 b/v0.8 new file mode 120000 index 0000000..4ea5caf --- /dev/null +++ b/v0.8 @@ -0,0 +1 @@ +v0.8.0 \ No newline at end of file diff --git a/v0.8.0/.documenter-siteinfo.json b/v0.8.0/.documenter-siteinfo.json new file mode 100644 index 0000000..4cd5aee --- /dev/null +++ b/v0.8.0/.documenter-siteinfo.json @@ -0,0 +1 @@ +{"documenter":{"julia_version":"1.7.3","generation_timestamp":"2024-05-22T06:20:26","documenter_version":"1.4.1"}} \ No newline at end of file diff --git a/v0.8.0/_common/getting_started_constraints/index.html b/v0.8.0/_common/getting_started_constraints/index.html new file mode 100644 index 0000000..368af69 --- /dev/null +++ b/v0.8.0/_common/getting_started_constraints/index.html @@ -0,0 +1,59 @@ + +- · Clarabel jl/rs
GitHub

The Clarabel interface expects constraints to be presented in the single vectorized form $Ax + s = b, s \in \mathcal{K}$, where $\mathcal{K} = \mathcal{K}_1 \times \dots \times \mathcal{K}_p$ and each $\mathcal{K}_i$ is one of the solver's supported cone types.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our constraints are:

  • A single equality constraint $x_1 + x_2 - x_3 = 1$.
  • A pair of inequalities such that $x_2$ and $x_3$ are each less than 2.
  • A second order cone constraint on the 3-dimensional vector $x$.

For the three constraints above, we have

\[ +\begin{align*} + +A_{eq} &= +\left[ +\begin{array}{lll} +1 & 1 & -1 +\end{array} +\right], +\quad & +b_{eq} &= +\left[ +\begin{array}{l} +1 +\end{array} +\right], + +\\[4ex] + +A_{ineq} &= +\left[ +\begin{array}{lll} +0 & 1 & 0 \\ +0 & 0 & 1 +\end{array} +\right], +\quad & +b_{ineq} &= +\left[ +\begin{array}{l} +2\\2 +\end{array} +\right], + +\\[4ex] + +A_{soc} &= +\left[ +\begin{array}{rrr} +-1 & 0 & 0 \\ + 0 & -1 & 0 \\ + 0 & 0 & -1 +\end{array} +\right], +\quad & +b_{soc} &= +\left[ +\begin{array}{l} +0 \\0 \\0 +\end{array} +\right] + +\end{align*} +\]

diff --git a/v0.8.0/_common/getting_started_constraints_note/index.html b/v0.8.0/_common/getting_started_constraints_note/index.html new file mode 100644 index 0000000..b2c56fe --- /dev/null +++ b/v0.8.0/_common/getting_started_constraints_note/index.html @@ -0,0 +1,6 @@ + +- · Clarabel jl/rs
GitHub
Note

Note carefully the signs in the above example. The inequality condition is $A_{ineq} x \le b_{ineq}$, which is equivalent to $A_{ineq} x + s = b_{ineq}$ with $s \ge 0$, i.e. $s$ in the Nonnegative cone. The SOC condition is $x \in \mathcal{K}_{SOC}$, or equivalently $-x + s = 0$ with $s \in \mathcal{K}_{SOC}$.

diff --git a/v0.8.0/_common/getting_started_objective/index.html b/v0.8.0/_common/getting_started_objective/index.html new file mode 100644 index 0000000..4dcba73 --- /dev/null +++ b/v0.8.0/_common/getting_started_objective/index.html @@ -0,0 +1,47 @@ + +- · Clarabel jl/rs
GitHub

To set the objective function of your optimisation problem simply define the square positive semidefinite matrix $P \in \mathrm{R}^{n\times n}$ and the vector $q \in \mathrm{R}^{n}$.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our objective function is:

\[\begin{equation*} +\min ~ +\frac{1}{2} +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +^T +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +1.0 & 4.0 & 2.0 \\ + -1.0 & 2.0 & 5.0 +\end{array} +\right] +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] ++ +\left[ +\begin{array}{r} +1 \\ 2 \\-3 +\end{array} +\right]^T +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +\end{equation*}\]

Clarabel expects the P matrix to be supplied in Compressed Sparse Column format. P is assumed by the solver to be symmetric and only values in the upper triangular part of P are needed by the solver, i.e. you only need to provide

\[\begin{equation*} +P = +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +⋅ & 4.0 & 2.0 \\ +⋅ & ⋅ & 5.0 +\end{array} +\right] +\end{equation*}\]

diff --git a/v0.8.0/_common/getting_started_problem/index.html b/v0.8.0/_common/getting_started_problem/index.html new file mode 100644 index 0000000..4d0edbe --- /dev/null +++ b/v0.8.0/_common/getting_started_problem/index.html @@ -0,0 +1,6 @@ + +- · Clarabel jl/rs
GitHub

Clarabel solves optimisation problems in the format:

\[\begin{array}{ll} \text{minimize} & \textstyle{\frac{1}{2}}x^\top Px + q^\top x\\ \text{subject to} & Ax + s = b \\ & s \in \mathcal{K}, \end{array}\]

with decision variables $x \in \mathbb{R}^n$, $s \in \mathbb{R}^m$ and data matrices $P=P^\top \succeq 0$, $q \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. The convex cone $\mathcal{K}$ is a composition of smaller convex cones $\mathcal{K} = \mathcal{K}_1 \times \mathcal{K}_2 \dots \mathcal{K}_p$. Equality conditions can be modelled in this format using the solver's ZeroCone type.

To initialize the solver with an optimisation problem we require three things:

  • The objective function, i.e. the matrix P and the vector q in $\frac{1}{2}x^\top P x + q^\top x$.
  • The data matrix A and vector b, along with a description of the composite cone $\mathcal{K}$ and the dimensions of its constituent pieces.
  • A settings object that specifies how Clarabel solves the problem.
diff --git a/v0.8.0/_common/getting_started_solution_warn/index.html b/v0.8.0/_common/getting_started_solution_warn/index.html new file mode 100644 index 0000000..170f6f5 --- /dev/null +++ b/v0.8.0/_common/getting_started_solution_warn/index.html @@ -0,0 +1,6 @@ + +- · Clarabel jl/rs
GitHub
Warning

Be careful to retrieve solver solutions from the solution that is returned by the solver, or directly from a solver object from the solver.solution field. Do not use the solver.variables, since these have both homogenization and equilibration scaling applied and therefore do not solve the optimization problem posed to the solver.

diff --git a/v0.8.0/api_cone_types/index.html b/v0.8.0/api_cone_types/index.html new file mode 100644 index 0000000..068331f --- /dev/null +++ b/v0.8.0/api_cone_types/index.html @@ -0,0 +1,6 @@ + +Supported Cone Types · Clarabel jl/rs
GitHub

Supported Cone Types

Clarabel natively supports optimization problems with conic constraints defined on the following cones:

Cone TypeConstructorDefinition
Zero coneZeroConeT(n)$\{ 0 \}^{n}$
Nonnegative OrthantNonnegativeConeT(n)$\{ x \in \mathbb{R}^{n} : x_i \ge 0, \forall i=1,\dots,\mathrm{n} \}$
Second-Order ConeSecondOrderConeT(n)$\{ (t,x) \in \mathbb{R}^{n} : ||x||_2 \leq t \}$
Exponential ConeExponentialConeT()$\{(x, y, z) : y > 0,~~ ye^{x/y} ≤ z \}$
Power ConePowerConeT(a)$\{(x, y, z) : x^a y^{(1-a)} \geq |z|,~ (x,y) \geq 0 \}$ with $a \in (0,1)$
Generalized Power ConeGenPowerConeT(a,n)$\{(x, y) \in \mathbb{R}^{len(a)} \times \mathbb{R}^{n} : \prod\limits_{a_i \in a} x_i^{a_i} \geq ||y||_2,~ x \ge 0 \}$ with $a_i \in (0,1)$ and $\sum a_i = 1$
Positive Semidefinite Cone (triangular part)PSDTriangleConeT(n)Upper triangular part of the positive semidefinite cone $\mathbb{S}^{n}_+$. The elements $x$ of this cone represent the columnwise stacking of the upper triangular part of a positive semidefinite matrix $X \in \mathbb{S}^{n}_+$, so that $x \in \mathbb{R}^d$ with $d = {n(n+1)}/{2}.$
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GitHub

Julia API Reference

Solver and main API

Clarabel.Solver — Type
Solver{T <: AbstractFloat}()

Initializes an empty Clarabel solver that can be filled with problem data using:

setup!(solver, P, q, A, b, cones, [settings]).
source
Clarabel.setup! — Function
setup!(solver, P, q, A, b, cones, [settings])

Populates a Solver with a cost function defined by P and q, and one or more conic constraints defined by A, b and a description of a conic constraint composed of cones whose types and dimensions are specified by cones.

The solver will be configured to solve the following optimization problem:

min   1/2 x'Px + q'x
+s.t.  Ax + s = b, s ∈ K

All data matrices must be sparse. The matrix P is assumed to be symmetric and positive semidefinite, and only the upper triangular part is used.

The cone K is a composite cone. To define the cone the user should provide a vector of cone specifications along with the appropriate dimensional information. For example, to generate a cone in the nonnegative orthant followed by a second order cone, use:

cones = [Clarabel.NonnegativeConeT(dim_1),
+         Clarabel.SecondOrderConeT(dim_2)]

If the argument 'cones' is constructed incrementally, the should should initialize it as an empty array of the supertype for all allowable cones, e.g.

cones = Clarabel.SupportedCone[]
+push!(cones,Clarabel.NonnegativeConeT(dim_1))
+...

The optional argument settings can be used to pass custom solver settings:

settings = Clarabel.Settings(verbose = true)
+setup!(model, P, q, A, b, cones, settings)

To solve the problem, you must make a subsequent call to solve!

source
Clarabel.solve! — Function
solve!(solver)

Computes the solution to the problem in a Clarabel.Solver previously defined in setup!.

source

SupportedCone

Clarabel.SupportedCone — Type
SupportedCone

An abstract type use by the Clarabel API used when passing cone specifications to the solver setup!. The currently supported concrete types are:

  • ZeroConeT : The zero cone. Used to define equalities.
  • NonnegativeConeT: The nonnegative orthant.
  • SecondOrderConeT: The second order / Lorentz / ice-cream cone.
  • ExponentialConeT: The exponential cone (in R^3)
  • PowerConeT : The power cone with power α (in R^3)
  • GenPowerConeT : The generalized power cone
  • PSDTriangleConeT: The positive semidefinite cone (triangular format).
source

Solver Status

Clarabel.SolverStatus — Type
SolverStatus

An Enum of of possible conditions set by solve!.

If no call has been made to solve!, then the SolverStatus is:

  • UNSOLVED: The algorithm has not started.

Otherwise:

  • SOLVED : Solver terminated with a solution.
  • PRIMAL_INFEASIBLE : Problem is primal infeasible. Solution returned is a certificate of primal infeasibility.
  • DUAL_INFEASIBLE : Problem is dual infeasible. Solution returned is a certificate of dual infeasibility.
  • ALMOST_SOLVED : Solver terminated with a solution (reduced accuracy).
  • ALMOST_PRIMAL_INFEASIBLE : Problem is primal infeasible. Solution returned is a certificate of primal infeasibility (reduced accuracy).
  • ALMOST_DUAL_INFEASIBLE : Problem is dual infeasible. Solution returned is a certificate of dual infeasibility (reduced accuracy).
  • MAX_ITERATIONS : Iteration limit reached before solution or infeasibility certificate found.
  • MAX_TIME : Time limit reached before solution or infeasibility certificate found.
  • NUMERICAL_ERROR : Solver terminated with a numerical error.
  • INSUFFICIENT_PROGRESS : Solver terminated due to lack of progress.
source
diff --git a/v0.8.0/api_rs/index.html b/v0.8.0/api_rs/index.html new file mode 100644 index 0000000..c856b6f --- /dev/null +++ b/v0.8.0/api_rs/index.html @@ -0,0 +1,13 @@ + +Rust API ⧉ · Clarabel jl/rs
GitHub
diff --git a/v0.8.0/api_settings/index.html b/v0.8.0/api_settings/index.html new file mode 100644 index 0000000..7cb838d --- /dev/null +++ b/v0.8.0/api_settings/index.html @@ -0,0 +1,6 @@ + +Solver Settings · Clarabel jl/rs
GitHub

Clarabel Solver Settings

The Clarabel solver supports a variety of configuration options. The Julia, Rust and Python and interfaces all support the same set of options with identical field names.

Warning

The solver defaults are configured to give good general performance for most problems, but assume that the problem data is of 64 bit float type. Although the Rust and Julia solvers will accept 32 bit types instead (i.e. Float32 in Julia or f32 in Rust), the solver is unlikely to perform well unless the tolerances are relaxed.

The full set of options follows below.

Settings

Clarabel.Settings — Type
ArgumentDefault ValueDescription
Main Algorithm Settings
max_iter200maximum number of iterations
time_limitInfmaximum run time (seconds)
verbosetrueverbose printing
max_step_fraction0.99maximum interior point step length
Full Accuracy Settings
tol_gap_abs1e-8absolute duality gap tolerance
tol_gap_rel1e-8relative duality gap tolerance
tol_feas1e-8feasibility check tolerance (primal and dual)
tol_infeas_abs1e-8absolute infeasibility tolerance (primal and dual)
tol_infeas_rel1e-8relative infeasibility tolerance (primal and dual)
tol_ktratio1e-6κ/τ tolerance
Reduced Accuracy Settings
reduced_tol_gap_abs5e-5reduced absolute duality gap tolerance
reduced_tol_gap_rel5e-5reduced relative duality gap tolerance
reduced_tol_feas1e-4reduced feasibility check tolerance (primal and dual)
reduced_tol_infeas_abs5e-5reduced absolute infeasibility tolerance (primal and dual)
reduced_tol_infeas_rel5e-5reduced relative infeasibility tolerance (primal and dual)
reduced_tol_ktratio1e-4reduced κ/τ tolerance
Data Equilibration Settings
equilibrate_enabletrueenable data equilibration pre-scaling
equilibrate_max_iter10maximum equilibration scaling iterations
equilibrate_min_scaling1e-4minimum equilibration scaling allowed
equilibrate_max_scaling1e+4maximum equilibration scaling allowed
Step Size Settings
linesearch_backtrack_step0.8linesearch backtracking
min_switch_step_length1e-1minimum step size allowed for asymmetric cones with PrimalDual scaling
min_terminate_step_length1e-4minimum step size allowed for symmetric cones & asymmetric cones with Dual scaling
Linear Solver Settings
direct_kkt_solvertrueuse a direct linear solver method (required true)
direct_solve_method:qdldldirect linear solver (e.g. :qdldl, :mkl, :panua, :ma57, :cholmod, :faer)
static_regularization_enabletrueenable KKT static regularization
static_regularization_eps1e-8KKT static regularization parameter
static_regularization_proportionaleps(T)^2additional regularization parameter w.r.t. the maximum abs diagonal term
dynamic_regularization_enabletrueenable KKT dynamic regularization
dynamic_regularization_eps1e-13KKT dynamic regularization threshold
dynamic_regularization_delta2e-7KKT dynamic regularization shift
iterative_refinement_enabletrueKKT direct solve with iterative refinement
iterative_refinement_reltol1e-12iterative refinement relative tolerance
iterative_refinement_abstol1e-12iterative refinement absolute tolerance
iterative_refinement_max_iter10iterative refinement maximum iterations
iterative_refinement_stop_ratio5.0iterative refinement stalling tolerance

Preprocessing Settings presolve_enable | true | enable presolve constraint reduction || __Chordal Decomposition Settings|| chordal_decomposition_enable | true | enable chordal decomposition chordal_decomposition_mergemethod | :cliquegraph | chordal decomposition merge method (:none, :parentchild or :cliquegraph) chordal_decomposition_compact | true | assemble decomposed system in "compact" form chordal_decomposition_complete_dual | false | complete PSD dual variables after decomposition

source
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100644 index 0000000..dafa1b0 --- /dev/null +++ b/v0.8.0/assets/custom.css @@ -0,0 +1,3 @@ +div#documenter .docs-sidebar .docs-logo > img { + max-width: 70em; +} diff --git a/v0.8.0/assets/documenter.js b/v0.8.0/assets/documenter.js new file mode 100644 index 0000000..c6562b5 --- /dev/null +++ b/v0.8.0/assets/documenter.js @@ -0,0 +1,1050 @@ +// Generated by Documenter.jl +requirejs.config({ + paths: { + 'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min', + 'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min', + 'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min', + 'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min', + 'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min', + 'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min', + 'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min', + 'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min', + 'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia-repl.min', + }, + shim: { + "highlight-julia": { + "deps": [ + "highlight" + ] + }, + "katex-auto-render": { + "deps": [ + "katex" + ] + }, + "headroom-jquery": { + "deps": [ + "jquery", + "headroom" + ] + }, + "highlight-julia-repl": { + "deps": [ + "highlight" + ] + } +} +}); +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) { +$(document).ready(function() { + renderMathInElement( + document.body, + { + "delimiters": [ + { + "left": "$", + "right": "$", + "display": false + }, + { + "left": "$$", + "right": "$$", + "display": true + }, + { + "left": "\\[", + "right": "\\]", + "display": true + } + ] +} + + ); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($) { +$(document).ready(function() { + hljs.highlightAll(); +}) + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +let timer = 0; +var isExpanded = true; + +$(document).on("click", ".docstring header", function () { + let articleToggleTitle = "Expand docstring"; + + debounce(() => { + if ($(this).siblings("section").is(":visible")) { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + } else { + $(this) + .find(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + articleToggleTitle = "Collapse docstring"; + } + + $(this) + .find(".docstring-article-toggle-button") + .prop("title", articleToggleTitle); + $(this).siblings("section").slideToggle(); + }); +}); + +$(document).on("click", ".docs-article-toggle-button", function (event) { + let articleToggleTitle = "Expand docstring"; + let navArticleToggleTitle = "Expand all docstrings"; + let animationSpeed = event.noToggleAnimation ? 0 : 400; + + debounce(() => { + if (isExpanded) { + $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-down") + .addClass("fa-chevron-right"); + + isExpanded = false; + + $(".docstring section").slideUp(animationSpeed); + } else { + $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up"); + $(".docstring-article-toggle-button") + .removeClass("fa-chevron-right") + .addClass("fa-chevron-down"); + + isExpanded = true; + articleToggleTitle = "Collapse docstring"; + navArticleToggleTitle = "Collapse all docstrings"; + + $(".docstring section").slideDown(animationSpeed); + } + + $(this).prop("title", navArticleToggleTitle); + $(".docstring-article-toggle-button").prop("title", articleToggleTitle); + }); +}); + +function debounce(callback, timeout = 300) { + if (Date.now() - timer > timeout) { + callback(); + } + + clearTimeout(timer); + + timer = Date.now(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require([], function() { +function addCopyButtonCallbacks() { + for (const el of document.getElementsByTagName("pre")) { + const button = document.createElement("button"); + button.classList.add("copy-button", "fa-solid", "fa-copy"); + button.setAttribute("aria-label", "Copy this code block"); + button.setAttribute("title", "Copy"); + + el.appendChild(button); + + const success = function () { + button.classList.add("success", "fa-check"); + button.classList.remove("fa-copy"); + }; + + const failure = function () { + button.classList.add("error", "fa-xmark"); + button.classList.remove("fa-copy"); + }; + + button.addEventListener("click", function () { + copyToClipboard(el.innerText).then(success, failure); + + setTimeout(function () { + button.classList.add("fa-copy"); + button.classList.remove("success", "fa-check", "fa-xmark"); + }, 5000); + }); + } +} + +function copyToClipboard(text) { + // clipboard API is only available in secure contexts + if (window.navigator && window.navigator.clipboard) { + return window.navigator.clipboard.writeText(text); + } else { + return new Promise(function (resolve, reject) { + try { + const el = document.createElement("textarea"); + el.textContent = text; + el.style.position = "fixed"; + el.style.opacity = 0; + document.body.appendChild(el); + el.select(); + document.execCommand("copy"); + + resolve(); + } catch (err) { + reject(err); + } finally { + document.body.removeChild(el); + } + }); + } +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks); +} else { + addCopyButtonCallbacks(); +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) { + +// Manages the top navigation bar (hides it when the user starts scrolling down on the +// mobile). +window.Headroom = Headroom; // work around buggy module loading? +$(document).ready(function () { + $("#documenter .docs-navbar").headroom({ + tolerance: { up: 10, down: 10 }, + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let meta = $("div[data-docstringscollapsed]").data(); + + if (meta?.docstringscollapsed) { + $("#documenter-article-toggle-button").trigger({ + type: "click", + noToggleAnimation: true, + }); + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +/* +To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc + +PSEUDOCODE: + +Searching happens automatically as the user types or adjusts the selected filters. +To preserve responsiveness, as much as possible of the slow parts of the search are done +in a web worker. Searching and result generation are done in the worker, and filtering and +DOM updates are done in the main thread. The filters are in the main thread as they should +be very quick to apply. This lets filters be changed without re-searching with minisearch +(which is possible even if filtering is on the worker thread) and also lets filters be +changed _while_ the worker is searching and without message passing (neither of which are +possible if filtering is on the worker thread) + +SEARCH WORKER: + +Import minisearch + +Build index + +On message from main thread + run search + find the first 200 unique results from each category, and compute their divs for display + note that this is necessary and sufficient information for the main thread to find the + first 200 unique results from any given filter set + post results to main thread + +MAIN: + +Launch worker + +Declare nonconstant globals (worker_is_running, last_search_text, unfiltered_results) + +On text update + if worker is not running, launch_search() + +launch_search + set worker_is_running to true, set last_search_text to the search text + post the search query to worker + +on message from worker + if last_search_text is not the same as the text in the search field, + the latest search result is not reflective of the latest search query, so update again + launch_search() + otherwise + set worker_is_running to false + + regardless, display the new search results to the user + save the unfiltered_results as a global + update_search() + +on filter click + adjust the filter selection + update_search() + +update_search + apply search filters by looping through the unfiltered_results and finding the first 200 + unique results that match the filters + + Update the DOM +*/ + +/////// SEARCH WORKER /////// + +function worker_function(documenterSearchIndex, documenterBaseURL, filters) { + importScripts( + "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js" + ); + + let data = documenterSearchIndex.map((x, key) => { + x["id"] = key; // minisearch requires a unique for each object + return x; + }); + + // list below is the lunr 2.1.3 list minus the intersect with names(Base) + // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with) + // ideally we'd just filter the original list but it's not available as a variable + const stopWords = new Set([ + "a", + "able", + "about", + "across", + "after", + "almost", + "also", + "am", + "among", + "an", + "and", + "are", + "as", + "at", + "be", + "because", + "been", + "but", + "by", + "can", + "cannot", + "could", + "dear", + "did", + "does", + "either", + "ever", + "every", + "from", + "got", + "had", + "has", + "have", + "he", + "her", + "hers", + "him", + "his", + "how", + "however", + "i", + "if", + "into", + "it", + "its", + "just", + "least", + "like", + "likely", + "may", + "me", + "might", + "most", + "must", + "my", + "neither", + "no", + "nor", + "not", + "of", + "off", + "often", + "on", + "or", + "other", + "our", + "own", + "rather", + "said", + "say", + "says", + "she", + "should", + "since", + "so", + "some", + "than", + "that", + "the", + "their", + "them", + "then", + "there", + "these", + "they", + "this", + "tis", + "to", + "too", + "twas", + "us", + "wants", + "was", + "we", + "were", + "what", + "when", + "who", + "whom", + "why", + "will", + "would", + "yet", + "you", + "your", + ]); + + let index = new MiniSearch({ + fields: ["title", "text"], // fields to index for full-text search + storeFields: ["location", "title", "text", "category", "page"], // fields to return with results + processTerm: (term) => { + let word = stopWords.has(term) ? null : term; + if (word) { + // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names + word = word + .replace(/^[^a-zA-Z0-9@!]+/, "") + .replace(/[^a-zA-Z0-9@!]+$/, ""); + + word = word.toLowerCase(); + } + + return word ?? null; + }, + // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not + // find anything if searching for "add!", only for the entire qualification + tokenize: (string) => string.split(/[\s\-\.]+/), + // options which will be applied during the search + searchOptions: { + prefix: true, + boost: { title: 100 }, + fuzzy: 2, + }, + }); + + index.addAll(data); + + /** + * Used to map characters to HTML entities. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const htmlEscapes = { + "&": "&", + "<": "<", + ">": ">", + '"': """, + "'": "'", + }; + + /** + * Used to match HTML entities and HTML characters. + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + const reUnescapedHtml = /[&<>"']/g; + const reHasUnescapedHtml = RegExp(reUnescapedHtml.source); + + /** + * Escape function from lodash + * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts + */ + function escape(string) { + return string && reHasUnescapedHtml.test(string) + ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr]) + : string || ""; + } + + /** + * Make the result component given a minisearch result data object and the value + * of the search input as queryString. To view the result object structure, refer: + * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult + * + * @param {object} result + * @param {string} querystring + * @returns string + */ + function make_search_result(result, querystring) { + let search_divider = `

`; + let display_link = + result.location.slice(Math.max(0), Math.min(50, result.location.length)) + + (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div + + if (result.page !== "") { + display_link += ` (${result.page})`; + } + + let textindex = new RegExp(`${querystring}`, "i").exec(result.text); + let text = + textindex !== null + ? result.text.slice( + Math.max(textindex.index - 100, 0), + Math.min( + textindex.index + querystring.length + 100, + result.text.length + ) + ) + : ""; // cut-off text before and after from the match + + text = text.length ? escape(text) : ""; + + let display_result = text.length + ? "..." + + text.replace( + new RegExp(`${escape(querystring)}`, "i"), // For first occurrence + '$&' + ) + + "..." + : ""; // highlights the match + + let in_code = false; + if (!["page", "section"].includes(result.category.toLowerCase())) { + in_code = true; + } + + // We encode the full url to escape some special characters which can lead to broken links + let result_div = ` + +
+
${escape(result.title)}
+
${result.category}
+
+

+ ${display_result} +

+
+ ${display_link} +
+ + ${search_divider} + `; + + return result_div; + } + + self.onmessage = function (e) { + let query = e.data; + let results = index.search(query, { + filter: (result) => { + // Only return relevant results + return result.score >= 1; + }, + }); + + // Pre-filter to deduplicate and limit to 200 per category to the extent + // possible without knowing what the filters are. + let filtered_results = []; + let counts = {}; + for (let filter of filters) { + counts[filter] = 0; + } + let present = {}; + + for (let result of results) { + cat = result.category; + cnt = counts[cat]; + if (cnt < 200) { + id = cat + "---" + result.location; + if (present[id]) { + continue; + } + present[id] = true; + filtered_results.push({ + location: result.location, + category: cat, + div: make_search_result(result, query), + }); + } + } + + postMessage(filtered_results); + }; +} + +// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript! +const filters = [ + ...new Set(documenterSearchIndex["docs"].map((x) => x.category)), +]; +const worker_str = + "(" + + worker_function.toString() + + ")(" + + JSON.stringify(documenterSearchIndex["docs"]) + + "," + + JSON.stringify(documenterBaseURL) + + "," + + JSON.stringify(filters) + + ")"; +const worker_blob = new Blob([worker_str], { type: "text/javascript" }); +const worker = new Worker(URL.createObjectURL(worker_blob)); + +/////// SEARCH MAIN /////// + +// Whether the worker is currently handling a search. This is a boolean +// as the worker only ever handles 1 or 0 searches at a time. +var worker_is_running = false; + +// The last search text that was sent to the worker. This is used to determine +// if the worker should be launched again when it reports back results. +var last_search_text = ""; + +// The results of the last search. This, in combination with the state of the filters +// in the DOM, is used compute the results to display on calls to update_search. +var unfiltered_results = []; + +// Which filter is currently selected +var selected_filter = ""; + +$(document).on("input", ".documenter-search-input", function (event) { + if (!worker_is_running) { + launch_search(); + } +}); + +function launch_search() { + worker_is_running = true; + last_search_text = $(".documenter-search-input").val(); + worker.postMessage(last_search_text); +} + +worker.onmessage = function (e) { + if (last_search_text !== $(".documenter-search-input").val()) { + launch_search(); + } else { + worker_is_running = false; + } + + unfiltered_results = e.data; + update_search(); +}; + +$(document).on("click", ".search-filter", function () { + if ($(this).hasClass("search-filter-selected")) { + selected_filter = ""; + } else { + selected_filter = $(this).text().toLowerCase(); + } + + // This updates search results and toggles classes for UI: + update_search(); +}); + +/** + * Make/Update the search component + */ +function update_search() { + let querystring = $(".documenter-search-input").val(); + + if (querystring.trim()) { + if (selected_filter == "") { + results = unfiltered_results; + } else { + results = unfiltered_results.filter((result) => { + return selected_filter == result.category.toLowerCase(); + }); + } + + let search_result_container = ``; + let modal_filters = make_modal_body_filters(); + let search_divider = `
`; + + if (results.length) { + let links = []; + let count = 0; + let search_results = ""; + + for (var i = 0, n = results.length; i < n && count < 200; ++i) { + let result = results[i]; + if (result.location && !links.includes(result.location)) { + search_results += result.div; + count++; + links.push(result.location); + } + } + + if (count == 1) { + count_str = "1 result"; + } else if (count == 200) { + count_str = "200+ results"; + } else { + count_str = count + " results"; + } + let result_count = `
${count_str}
`; + + search_result_container = ` +
+ ${modal_filters} + ${search_divider} + ${result_count} +
+ ${search_results} +
+
+ `; + } else { + search_result_container = ` +
+ ${modal_filters} + ${search_divider} +
0 result(s)
+
+
No result found!
+ `; + } + + if ($(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").removeClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(search_result_container); + } else { + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".search-modal-card-body").html(` +
Type something to get started!
+ `); + } +} + +/** + * Make the modal filter html + * + * @returns string + */ +function make_modal_body_filters() { + let str = filters + .map((val) => { + if (selected_filter == val.toLowerCase()) { + return `${val}`; + } else { + return `${val}`; + } + }) + .join(""); + + return ` +
+ Filters: + ${str} +
`; +} + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Modal settings dialog +$(document).ready(function () { + var settings = $("#documenter-settings"); + $("#documenter-settings-button").click(function () { + settings.toggleClass("is-active"); + }); + // Close the dialog if X is clicked + $("#documenter-settings button.delete").click(function () { + settings.removeClass("is-active"); + }); + // Close dialog if ESC is pressed + $(document).keyup(function (e) { + if (e.keyCode == 27) settings.removeClass("is-active"); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +$(document).ready(function () { + let search_modal_header = ` +
+
+

+ + + + +

+
+
+ +
+
+ `; + + let initial_search_body = ` +
Type something to get started!
+ `; + + let search_modal_footer = ` +
+ + Ctrl + + / to search + + esc to close +
+ `; + + $(document.body).append( + ` + + ` + ); + + document.querySelector(".docs-search-query").addEventListener("click", () => { + openModal(); + }); + + document + .querySelector(".close-search-modal") + .addEventListener("click", () => { + closeModal(); + }); + + $(document).on("click", ".search-result-link", function () { + closeModal(); + }); + + document.addEventListener("keydown", (event) => { + if ((event.ctrlKey || event.metaKey) && event.key === "/") { + openModal(); + } else if (event.key === "Escape") { + closeModal(); + } + + return false; + }); + + // Functions to open and close a modal + function openModal() { + let searchModal = document.querySelector("#search-modal"); + + searchModal.classList.add("is-active"); + document.querySelector(".documenter-search-input").focus(); + } + + function closeModal() { + let searchModal = document.querySelector("#search-modal"); + let initial_search_body = ` +
Type something to get started!
+ `; + + searchModal.classList.remove("is-active"); + document.querySelector(".documenter-search-input").blur(); + + if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) { + $(".search-modal-card-body").addClass("is-justify-content-center"); + } + + $(".documenter-search-input").val(""); + $(".search-modal-card-body").html(initial_search_body); + } + + document + .querySelector("#search-modal .modal-background") + .addEventListener("click", () => { + closeModal(); + }); +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Manages the showing and hiding of the sidebar. +$(document).ready(function () { + var sidebar = $("#documenter > .docs-sidebar"); + var sidebar_button = $("#documenter-sidebar-button"); + sidebar_button.click(function (ev) { + ev.preventDefault(); + sidebar.toggleClass("visible"); + if (sidebar.hasClass("visible")) { + // Makes sure that the current menu item is visible in the sidebar. + $("#documenter .docs-menu a.is-active").focus(); + } + }); + $("#documenter > .docs-main").bind("click", function (ev) { + if ($(ev.target).is(sidebar_button)) { + return; + } + if (sidebar.hasClass("visible")) { + sidebar.removeClass("visible"); + } + }); +}); + +// Resizes the package name / sitename in the sidebar if it is too wide. +// Inspired by: https://github.com/davatron5000/FitText.js +$(document).ready(function () { + e = $("#documenter .docs-autofit"); + function resize() { + var L = parseInt(e.css("max-width"), 10); + var L0 = e.width(); + if (L0 > L) { + var h0 = parseInt(e.css("font-size"), 10); + e.css("font-size", (L * h0) / L0); + // TODO: make sure it survives resizes? + } + } + // call once and then register events + resize(); + $(window).resize(resize); + $(window).on("orientationchange", resize); +}); + +// Scroll the navigation bar to the currently selected menu item +$(document).ready(function () { + var sidebar = $("#documenter .docs-menu").get(0); + var active = $("#documenter .docs-menu .is-active").get(0); + if (typeof active !== "undefined") { + sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15; + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// Theme picker setup +$(document).ready(function () { + // onchange callback + $("#documenter-themepicker").change(function themepick_callback(ev) { + var themename = $("#documenter-themepicker option:selected").attr("value"); + if (themename === "auto") { + // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light'); + window.localStorage.removeItem("documenter-theme"); + } else { + // set_theme(themename); + window.localStorage.setItem("documenter-theme", themename); + } + // We re-use the global function from themeswap.js to actually do the swapping. + set_theme_from_local_storage(); + }); + + // Make sure that the themepicker displays the correct theme when the theme is retrieved + // from localStorage + if (typeof window.localStorage !== "undefined") { + var theme = window.localStorage.getItem("documenter-theme"); + if (theme !== null) { + $("#documenter-themepicker option").each(function (i, e) { + e.selected = e.value === theme; + }); + } + } +}); + +}) +//////////////////////////////////////////////////////////////////////////////// +require(['jquery'], function($) { + +// update the version selector with info from the siteinfo.js and ../versions.js files +$(document).ready(function () { + // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the + // siteinfo.js file, we just return immediately and not display the version selector. + if ( + typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" && + DOCUMENTER_VERSION_SELECTOR_DISABLED + ) { + return; + } + + var version_selector = $("#documenter .docs-version-selector"); + var version_selector_select = $("#documenter .docs-version-selector select"); + + version_selector_select.change(function (x) { + target_href = version_selector_select + .children("option:selected") + .get(0).value; + window.location.href = target_href; + }); + + // add the current version to the selector based on siteinfo.js, but only if the selector is empty + if ( + typeof DOCUMENTER_CURRENT_VERSION !== "undefined" && + $("#version-selector > option").length == 0 + ) { + var option = $( + "" + ); + version_selector_select.append(option); + } + + if (typeof DOC_VERSIONS !== "undefined") { + var existing_versions = version_selector_select.children("option"); + var existing_versions_texts = existing_versions.map(function (i, x) { + return x.text; + }); + DOC_VERSIONS.forEach(function (each) { + var version_url = documenterBaseURL + "/../" + each + "/"; + var existing_id = $.inArray(each, existing_versions_texts); + // if not already in the version selector, add it as a new option, + // otherwise update the old option with the URL and enable it + if (existing_id == -1) { + var option = $( + "" + ); + version_selector_select.append(option); + } else { + var option = existing_versions[existing_id]; + option.value = version_url; + option.disabled = false; + } + }); + } + + // only show the version selector if the selector has been populated + if (version_selector_select.children("option").length > 0) { + version_selector.toggleClass("visible"); + } +}); + +}) diff --git a/v0.8.0/assets/favicon.ico b/v0.8.0/assets/favicon.ico new file mode 100644 index 0000000000000000000000000000000000000000..7b4dd20af498487395f7620b7874ff727e48b5de GIT binary patch literal 24428 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kbd.button.is-inverted.is-outlined{background-color:transparent;border-color:#fff;box-shadow:none;color:#fff}html.theme--documenter-dark .button.is-primary,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink{background-color:#375a7f;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:hover,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:hover,html.theme--documenter-dark .button.is-primary.is-hovered,html.theme--documenter-dark .docstring>section>a.button.is-hovered.docs-sourcelink{background-color:#335476;border-color:transparent;color:#fff}html.theme--documenter-dark .button.is-primary:focus,html.theme--documenter-dark .docstring>section>a.button.docs-sourcelink:focus,html.theme--documenter-dark .button.is-primary.is-focused,html.theme--documenter-dark .docstring>section>a.button.is-focused.docs-sourcelink{border-color:transparent;color:#fff}html.theme--documenter-dark 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h1,html.theme--documenter-dark .content h2,html.theme--documenter-dark .content h3,html.theme--documenter-dark .content h4,html.theme--documenter-dark .content h5,html.theme--documenter-dark .content h6{color:#f2f2f2;font-weight:600;line-height:1.125}html.theme--documenter-dark .content h1{font-size:2em;margin-bottom:0.5em}html.theme--documenter-dark .content h1:not(:first-child){margin-top:1em}html.theme--documenter-dark .content h2{font-size:1.75em;margin-bottom:0.5714em}html.theme--documenter-dark .content h2:not(:first-child){margin-top:1.1428em}html.theme--documenter-dark .content h3{font-size:1.5em;margin-bottom:0.6666em}html.theme--documenter-dark .content h3:not(:first-child){margin-top:1.3333em}html.theme--documenter-dark .content h4{font-size:1.25em;margin-bottom:0.8em}html.theme--documenter-dark .content h5{font-size:1.125em;margin-bottom:0.8888em}html.theme--documenter-dark .content h6{font-size:1em;margin-bottom:1em}html.theme--documenter-dark .content 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html.theme--documenter-dark .navbar-dropdown,html.theme--documenter-dark .navbar-dropdown.is-boxed{border-radius:8px;border-top:none;box-shadow:0 8px 8px rgba(10,10,10,0.1), 0 0 0 1px rgba(10,10,10,0.1);display:block;opacity:0;pointer-events:none;top:calc(100% + (-4px));transform:translateY(-5px);transition-duration:86ms;transition-property:opacity, transform}html.theme--documenter-dark .navbar-dropdown.is-right{left:auto;right:0}html.theme--documenter-dark .navbar-divider{display:block}html.theme--documenter-dark .navbar>.container .navbar-brand,html.theme--documenter-dark .container>.navbar .navbar-brand{margin-left:-.75rem}html.theme--documenter-dark .navbar>.container .navbar-menu,html.theme--documenter-dark .container>.navbar .navbar-menu{margin-right:-.75rem}html.theme--documenter-dark .navbar.is-fixed-bottom-desktop,html.theme--documenter-dark .navbar.is-fixed-top-desktop{left:0;position:fixed;right:0;z-index:30}html.theme--documenter-dark 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a.navbar-item.is-active:not(:focus):not(:hover),html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover){background-color:rgba(0,0,0,0)}html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link,html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link{background-color:rgba(0,0,0,0)}}html.theme--documenter-dark .hero.is-fullheight-with-navbar{min-height:calc(100vh - 4rem)}html.theme--documenter-dark .pagination{font-size:1rem;margin:-.25rem}html.theme--documenter-dark .pagination.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.pagination{font-size:.75rem}html.theme--documenter-dark .pagination.is-medium{font-size:1.25rem}html.theme--documenter-dark .pagination.is-large{font-size:1.5rem}html.theme--documenter-dark .pagination.is-rounded .pagination-previous,html.theme--documenter-dark #documenter .docs-sidebar 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.hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem} diff --git a/v0.8.0/assets/themeswap.js b/v0.8.0/assets/themeswap.js new file mode 100644 index 0000000..9f5eebe --- /dev/null +++ b/v0.8.0/assets/themeswap.js @@ -0,0 +1,84 @@ +// Small function to quickly swap out themes. Gets put into the tag.. +function set_theme_from_local_storage() { + // Initialize the theme to null, which means default + var theme = null; + // If the browser supports the localstorage and is not disabled then try to get the + // documenter theme + if (window.localStorage != null) { + // Get the user-picked theme from localStorage. May be `null`, which means the default + // theme. + theme = window.localStorage.getItem("documenter-theme"); + } + // Check if the users preference is for dark color scheme + var darkPreference = + window.matchMedia("(prefers-color-scheme: dark)").matches === true; + // Initialize a few variables for the loop: + // + // - active: will contain the index of the theme that should be active. Note that there + // is no guarantee that localStorage contains sane values. If `active` stays `null` + // we either could not find the theme or it is the default (primary) theme anyway. + // Either way, we then need to stick to the primary theme. + // + // - disabled: style sheets that should be disabled (i.e. all the theme style sheets + // that are not the currently active theme) + var active = null; + var disabled = []; + var primaryLightTheme = null; + var primaryDarkTheme = null; + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // To distinguish the default (primary) theme, it needs to have the data-theme-primary + // attribute set. + if (ss.ownerNode.getAttribute("data-theme-primary") !== null) { + primaryLightTheme = themename; + } + // Check if the theme is primary dark theme so that we could store its name in darkTheme + if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) { + primaryDarkTheme = themename; + } + // If we find a matching theme (and it's not the default), we'll set active to non-null + if (themename === theme) active = i; + // Store the style sheets of inactive themes so that we could disable them + if (themename !== theme) disabled.push(ss); + } + var activeTheme = null; + if (active !== null) { + // If we did find an active theme, we'll (1) add the theme--$(theme) class to + document.getElementsByTagName("html")[0].className = "theme--" + theme; + activeTheme = theme; + } else { + // If we did _not_ find an active theme, then we need to fall back to the primary theme + // which can either be dark or light, depending on the user's OS preference. + var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme; + // In case it somehow happens that the relevant primary theme was not found in the + // preceding loop, we abort without doing anything. + if (activeTheme === null) { + console.error("Unable to determine primary theme."); + return; + } + // When switching to the primary light theme, then we must not have a class name + // for the tag. That's only for non-primary or the primary dark theme. + if (darkPreference) { + document.getElementsByTagName("html")[0].className = + "theme--" + activeTheme; + } else { + document.getElementsByTagName("html")[0].className = ""; + } + } + for (var i = 0; i < document.styleSheets.length; i++) { + var ss = document.styleSheets[i]; + // The tag of each style sheet is expected to have a data-theme-name attribute + // which must contain the name of the theme. The names in localStorage much match this. + var themename = ss.ownerNode.getAttribute("data-theme-name"); + // attribute not set => non-theme stylesheet => ignore + if (themename === null) continue; + // we'll disable all the stylesheets, except for the active one + ss.disabled = !(themename == activeTheme); + } +} +set_theme_from_local_storage(); diff --git a/v0.8.0/assets/warner.js b/v0.8.0/assets/warner.js new file mode 100644 index 0000000..3f6f5d0 --- /dev/null +++ b/v0.8.0/assets/warner.js @@ -0,0 +1,52 @@ +function maybeAddWarning() { + // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE + // in siteinfo.js. + // If either of these are undefined something went horribly wrong, so we abort. + if ( + window.DOCUMENTER_NEWEST === undefined || + window.DOCUMENTER_CURRENT_VERSION === undefined || + window.DOCUMENTER_STABLE === undefined + ) { + return; + } + + // Current version is not a version number, so we can't tell if it's the newest version. Abort. + if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) { + return; + } + + // Current version is newest version, so no need to add a warning. + if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) { + return; + } + + // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs. + if (document.body.querySelector('meta[name="robots"]') === null) { + const meta = document.createElement("meta"); + meta.name = "robots"; + meta.content = "noindex"; + + document.getElementsByTagName("head")[0].appendChild(meta); + } + + const div = document.createElement("div"); + div.classList.add("outdated-warning-overlay"); + const closer = document.createElement("button"); + closer.classList.add("outdated-warning-closer", "delete"); + closer.addEventListener("click", function () { + document.body.removeChild(div); + }); + const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE; + div.innerHTML = + 'This documentation is not for the latest stable release, but for either the development version or an older release.
Click here to go to the documentation for the latest stable release.'; + div.appendChild(closer); + document.body.appendChild(div); +} + +if (document.readyState === "loading") { + document.addEventListener("DOMContentLoaded", maybeAddWarning); +} else { + maybeAddWarning(); +} diff --git a/v0.8.0/citing/index.html b/v0.8.0/citing/index.html new file mode 100644 index 0000000..8a36a3b --- /dev/null +++ b/v0.8.0/citing/index.html @@ -0,0 +1,31 @@ + +Citing Clarabel · Clarabel jl/rs

GitHub

If you find Clarabel useful in your work, please consider citing one or more of the following papers. For the solver itself:

@misc{Clarabel_2024,
+      title={Clarabel: An interior-point solver for conic programs with quadratic objectives}, 
+      author={Paul J. Goulart and Yuwen Chen},
+      year={2024},
+      eprint={2405.12762},
+      archivePrefix={arXiv},
+      primaryClass={math.OC}
+}

A preprint is available here.

If you use Clarabel to solve SDPs with decomposable structure:

@InProceedings{Garstka_2020,
+  author  = {Michael Garstka and Mark Cannon and Paul Goulart},
+  title   = {A clique graph based merging strategy for decomposable {SDPs}},
+  year    = {2020},
+  note    = {21th IFAC World Congress},
+  number  = {2},
+  pages   = {7355-7361},
+  volume  = {53},
+  doi     = {10.1016/j.ifacol.2020.12.1255},
+  issn    = {2405-8963},
+  journal = {IFAC-PapersOnLine},
+}

A preprint is available here.

If you use Clarabel to solve problems with generalized power cones:

@misc{chen2023efficient,
+      title={An Efficient IPM Implementation for A Class of Nonsymmetric Cones}, 
+      author={Yuwen Chen and Paul Goulart},
+      year={2023},
+      eprint={2305.12275},
+      archivePrefix={arXiv},
+      primaryClass={math.OC}
+}

A preprint is available here.

diff --git a/v0.8.0/contributing/index.html b/v0.8.0/contributing/index.html new file mode 100644 index 0000000..f7ff601 --- /dev/null +++ b/v0.8.0/contributing/index.html @@ -0,0 +1,6 @@ + +Contributing · Clarabel jl/rs
GitHub

Contributing

Contributions are always welcome:

  • Please report any issues and bugs that you encounter in Issues.

  • As an open source project we are also interested in any projects and applications that use Clarabel. Please let us know via email to: paul.goulart@eng.ox.ac.uk.

diff --git a/v0.8.0/examples/example_expcone/index.html b/v0.8.0/examples/example_expcone/index.html new file mode 100644 index 0000000..97750ee --- /dev/null +++ b/v0.8.0/examples/example_expcone/index.html @@ -0,0 +1,25 @@ + +Problem Description · Clarabel jl/rs
GitHub

Exponential Cone Example

In this example we show how to model optimization problems with exponential cone constraints. The exponential cone is defined as

\[\begin{aligned} +\mathcal{K}_{exp} =& \{(x, y, z) \mid y \geq 0,~ ye^{x/y} \le z\} ~\cup~ \\ +& \{ (x,y,z) \mid x \leq 0, y = 0, z \geq 0 \} +\end{aligned}\]

We will solve the following optimization problem:

\[\begin{array}{ll} \text{maximize} &x\\[2ex] +\text{subject to} & +\begin{array}{rl} +y e^{x / y} &\!\le~z \\ +y \!&=~1\\ +z \!&=~e^5. +\end{array} +\end{array}\]

Objective function

The Clarabel solver's default configuration expects problems to be posed as minimization problems, so we define:

\[P = 0 +\textrm{~~~and~~~} +q = - +\begin{bmatrix} 1 & 0 & 0 +\end{bmatrix}^T.\]

Constraints

The solver's default configuration expects constraints in the form $Ax + s = b$, where $s$ is in a cone or composition of cones. In this case we can write

\[\begin{bmatrix} 0 \\ 0 \\ 0 +\end{bmatrix} + - I +\begin{bmatrix} x \\ y \\ z +\end{bmatrix} = s +\in \mathcal{K}_{exp},\]

and then append the two additional equality constraints.

diff --git a/v0.8.0/examples/example_powcone/index.html b/v0.8.0/examples/example_powcone/index.html new file mode 100644 index 0000000..e961a5e --- /dev/null +++ b/v0.8.0/examples/example_powcone/index.html @@ -0,0 +1,20 @@ + +Problem Description · Clarabel jl/rs
GitHub

Power Cone Example

In this example we show how to model optimization problems with 3-dimensional power cone constraints. The power cone is defined as

\[`\mathcal{K}_{pow}(\alpha) = \{(x, y, z) \mid x^\alpha y^{(1-\alpha)} +\geq |z|, (x,y) \geq 0 \} \]

with $\alpha \in (0,1)$.

We will solve the following optimization problem:

\[\begin{array}{ll} \text{maximize} & x_1^{0.6} y^{0.4} + x_2^{0.1}\\[2ex] +\text{subject to} & +\begin{array}{rl} +(x_1, y, x_2) &\ge 0 \\ +x_1 + 2y + 3x_2 &= 3 +\end{array} +\end{array}\]

which is equivalent to

\[\begin{array}{ll} \text{maximize} & z_1 + z_2\\[2ex] +\text{subject to} & +\begin{array}{rl} +(x1, y, z1) &\in~\mathcal{K}_{pow}(0.6) \\ +(x2, 1, z2) &\in~\mathcal{K}_{pow}(0.1) \\ +x_1 + 2y + 3x_2 &=~3. +\end{array} +\end{array}\]

diff --git a/v0.8.0/examples/example_qp/index.html b/v0.8.0/examples/example_qp/index.html new file mode 100644 index 0000000..6613314 --- /dev/null +++ b/v0.8.0/examples/example_qp/index.html @@ -0,0 +1,14 @@ + +Problem Description · Clarabel jl/rs
GitHub

QP Example

Suppose that we want to solve the following 2-dimensional quadratic programming problem:

\[\begin{array}{ll} \text{minimize} & 3x_1^2 + 2x_2^2 - x_1 - 4x_2\\ +\text{subject to} & -1 \leq x \leq 1, ~ x_1 = 2x_2 +\end{array}\]

We will show how to solve this problem through each of Clarabel's supported languages and interfaces.

In each case the first step is to put the problem data into the standard form expected by the solver.

Objective function

The Clarabel solver's default configuration expects problem data in the form $\frac{1}{2}x^\top P x + q^\top x$. We therefore define the objective function data as

\[P = 2 \cdot \begin{bmatrix} 3 & 0 \\ 0 & 2\end{bmatrix} +\textrm{~~~and~~~} +q = \begin{bmatrix} -1 \\ -4\end{bmatrix}.\]

Constraints

The solver's default configuration expects constraints in the form $Ax + s = b$, where $s \in \mathcal{K}$ for some composite cone $\mathcal{K}$. We have 1 equality constraint and 4 inequalities, so we require the first element of $s$ to be zero (i.e. the first constraint will correspond to the equality) and all other elements $s_i \ge 0$. Our cone constraint on $s$ is therefore

\[s \in \mathcal K = \{0\}^1 \times \mathbb{R}^4_{\ge 0}.\]

Define the constraint data as

\[A = +\footnotesize\begin{bmatrix*}[r] 1 & -2 \\ 1 & 0 \\ 0 & 1 \\ -1 & 0 \\ 0 & -1\end{bmatrix*} +\textrm{~~~and~~~} + b= +\footnotesize\begin{bmatrix} 0 \\ 1 \\ 1 \\ 1 \\ 1 \end{bmatrix}.\]

Note that Clarabel expects inputs in Compressed Sparse Column (CSC) format for both $P$ and $A$.

diff --git a/v0.8.0/examples/example_sdp/index.html b/v0.8.0/examples/example_sdp/index.html new file mode 100644 index 0000000..195fca6 --- /dev/null +++ b/v0.8.0/examples/example_sdp/index.html @@ -0,0 +1,34 @@ + +Problem Description · Clarabel jl/rs
GitHub

Semidefinite Program (SDP) Example

In this example we show how to model semidefinite programming problems, i.e. problems defined with constraints on the symmetric positive semidefinite cone.

Given some symmetric matrix $X \in \mathbb{R}^{n\times n}$, Clarabel takes only the upper triangular vector of $n(n+1)/2$ entries when imposing semidefinite constraints. For example, given a $3 \times 3$ symmetric matrix variable

\[X = \begin{bmatrix} +x_1 & x_2 & x_4 \\ +x_2 & x_3 & x_5 \\ +x_4 & x_5 & x_6 +\end{bmatrix}\]

we would take as our decision variable the 6 element vector

\[x = +\begin{bmatrix} +x_1 & x_2 & x_3 & x_4 & x_5 & x_6 +\end{bmatrix}.\]

We define an operation

\[\textrm{vec}(X) = +\begin{bmatrix} +x_1 & \sqrt{2}x_2 & x_3 & \sqrt{2}x_4 & \sqrt{2}x_5 & x_6 +\end{bmatrix}\]

on symmetric matrices such that inner products are preserved, i.e. $\textrm{tr}(AB) = \textrm{vec}(A)^T\textrm{vec}(B)$, and will use the relationship

\[S \in \mathbb{R}^{n} \quad \Longleftrightarrow \quad \textrm{vec}(S) \in \mathcal{K}_{\text{tri}}^n\]

where $\mathcal{K}_{\text{tri}}^n$ is the positive semidefinite triangle cone.

Problem statement

We will solve the following optimization problem:

\[\begin{array}{ll} \text{minimize} &\textrm{trace}(X)\\[2ex] +\text{subject to} & +\begin{gathered} +\langle A,X\rangle = 1 \\ +X \succeq 0 +\end{gathered} +\end{array}\]

where $X = X^T \in\mathbb{R}^{3\times 3}$ and the symmetric matrix $A$ is defined as

\[A = \begin{bmatrix} +1 & 2 & 4 \\ +2 & 3 & 5 \\ +4 & 5 & 6 +\end{bmatrix}\]

Objective function

We can model the trace of the matrix $X$ by defining our objective function as

\[\frac{1}{2}x^TPx + q^Tx \]

with $P = 0$ and $q = \begin{bmatrix} 1 & 0 & 1 & 0 & 0 & 1 \end{bmatrix}^T$, where the elements of $q$ are chosen to select those elements of $x$ corresonding to the diagonal of the matrix $X$.

Constraints

The solver's default configuration expects constraints in the form $Ax + s = b$. In this we can write our semidefiniteness constraint as

\[-\text{vec}(X) = s \in \mathcal{K}_{\text{tri}}^n\]

where $\mathcal{K}_{\text{tri}}^n$ is the cone of vectors representing the triangular part of matrices in $\mathbb{S}_+^n$.

For the equality constraint can we must be careful to rewrite the inner product on $X$ in a form that is an equivalent linear function of $x$. We therefore write

\[\begin{aligned} + \langle A,X\rangle &= \textrm{vec}(A)^T\textrm{vec}(X) \\ + &= \begin{bmatrix} +1 & (2\cdot 2) & 3 & (2\cdot 4) & (2\cdot 5) & 6 +\end{bmatrix} +\begin{bmatrix} +x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5 \\ x_6 +\end{bmatrix} = 1. +\end{aligned}\]

diff --git a/v0.8.0/examples/example_socp/index.html b/v0.8.0/examples/example_socp/index.html new file mode 100644 index 0000000..11d04af --- /dev/null +++ b/v0.8.0/examples/example_socp/index.html @@ -0,0 +1,13 @@ + +Problem Description · Clarabel jl/rs
GitHub

SOCP Example

Suppose that we want to solve the following 2-dimensional optimization problem:

\[\begin{array}{ll} \text{minimize} & x_2^2\\[2ex] +\text{subject to} & \left\|\begin{pmatrix} 2x_1 \\ x_2 \end{pmatrix} +- \begin{pmatrix} 2 \\ 2 \end{pmatrix}\right\|_2 \le 1 +\end{array}\]

We will show how to solve this problem through each of Clarabel's supported languages and interfaces.

Objective function

The Clarabel solver's default configuration expects problem data in the form $\frac{1}{2}x^\top P x + q^\top x$. We therefore define the objective function data as

\[P = 2 \cdot \begin{bmatrix} 0 & 0 \\ 0 & 1\end{bmatrix} +\textrm{~~~and~~~} +q = \begin{bmatrix} 0 \\ 0\end{bmatrix}.\]

Constraints

The solver's default configuration expects constraints in the form $Ax + s = b$, where $s \in \mathcal{K}$ for some composite cone $\mathcal{K}$. We have a single constraint on the 2-norm of a vector, so we rewrite

\[\left\|\begin{pmatrix} 2x_1 \\ x_2 \end{pmatrix} - \begin{pmatrix} 2 \\ 2 \end{pmatrix}\right\|_2 \le 1 +\quad \Longleftrightarrow \quad +\begin{pmatrix} 1 \\ 2x_1 - 2\\ x_2 - 2 \end{pmatrix} \in \mathcal{K}_{SOC}\]

which puts our constraint in the form $b - Ax \in \mathcal{K}_{SOC}$.

diff --git a/v0.8.0/examples/jl/.gitignore b/v0.8.0/examples/jl/.gitignore new file mode 100644 index 0000000..1d8f445 --- /dev/null +++ b/v0.8.0/examples/jl/.gitignore @@ -0,0 +1 @@ +example_*.md \ No newline at end of file diff --git a/v0.8.0/examples/jl/README/index.html b/v0.8.0/examples/jl/README/index.html new file mode 100644 index 0000000..c461ebf --- /dev/null +++ b/v0.8.0/examples/jl/README/index.html @@ -0,0 +1,6 @@ + +- · Clarabel jl/rs
GitHub

Julia examples in this directory are automatically built from the <repo>/examples/jl using the Literate.jl package during documentation build.

diff --git a/v0.8.0/examples/jl/example_expcone/index.html b/v0.8.0/examples/jl/example_expcone/index.html new file mode 100644 index 0000000..59c90b6 --- /dev/null +++ b/v0.8.0/examples/jl/example_expcone/index.html @@ -0,0 +1,79 @@ + +Julia · Clarabel jl/rs
GitHub
using Clarabel, SparseArrays
+
+P = spzeros(3,3)
+
+q = [-1.,0.,0.]
+
+A = sparse([
+     -1.  0.  0.;
+      0. -1.  0.;
+      0.  0. -1.;
+      0.  1.  0.;
+      0.  0.  1.]);
+
+b = [0.,0.,0.,1.,exp(5.)];
+
+cones  = [Clarabel.ExponentialConeT(), Clarabel.ZeroConeT(2)]
+
+solver = Clarabel.Solver()
+
+settings = Clarabel.Settings()
+
+Clarabel.setup!(solver, P, q, A, b, cones, settings)
+
+result = Clarabel.solve!(solver)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 3
+  constraints   = 5
+  nnz(P)        = 0
+  nnz(A)        = 5
+  cones (total) = 2
+    : Zero        = 1,  numel = 2
+    : Exponential = 1,  numel = 3
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0   0.0000e+00  -0.0000e+00  0.00e+00  9.89e-01  5.04e-01  1.00e+00  1.00e+00   ------
+  1   3.3353e+00   6.8900e+00  1.07e+00  9.14e-01  8.95e-02  4.53e+00  2.14e-01  7.92e-01
+  2   1.5946e+01   3.3184e+01  1.08e+00  6.60e-01  1.78e-02  1.81e+01  4.59e-02  7.92e-01
+  3   2.4261e+01   5.1084e+01  1.11e+00  2.30e-01  5.04e-03  2.73e+01  1.13e-02  7.92e-01
+  4   7.1045e+00   1.3831e+01  9.47e-01  5.63e-02  1.50e-03  6.88e+00  3.38e-03  7.92e-01
+  5  -1.9077e+00  -4.4928e-01  1.46e+00  1.14e-02  3.05e-04  1.49e+00  7.24e-04  7.92e-01
+  6  -4.2883e+00  -3.9751e+00  7.88e-02  2.42e-03  6.44e-05  3.20e-01  1.55e-04  7.92e-01
+  7  -4.9836e+00  -4.9749e+00  1.76e-03  6.68e-05  1.78e-06  8.95e-03  4.30e-06  9.80e-01
+  8  -4.9996e+00  -4.9993e+00  4.91e-05  1.85e-06  4.94e-08  2.51e-04  1.19e-07  9.80e-01
+  9  -5.0000e+00  -5.0000e+00  1.38e-06  5.14e-08  1.37e-09  7.03e-06  3.31e-09  9.80e-01
+ 10  -5.0000e+00  -5.0000e+00  3.84e-08  1.43e-09  3.80e-11  1.96e-07  9.19e-11  9.80e-01
+ 11  -5.0000e+00  -5.0000e+00  8.23e-09  3.06e-10  8.14e-12  4.21e-08  1.97e-11  7.92e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time = 52.1ms
>>> Clarabel - Results
+Status: SOLVED
+Iterations: 11
+Objective: -5.000
+Solve time: 52.1ms
+
result.x
3-element Vector{Float64}:
+   4.9999999407684355
+   0.9999999990781195
+ 148.41315896637963

This page was generated using Literate.jl.

diff --git a/v0.8.0/examples/jl/example_intro/index.html b/v0.8.0/examples/jl/example_intro/index.html new file mode 100644 index 0000000..45d5c72 --- /dev/null +++ b/v0.8.0/examples/jl/example_intro/index.html @@ -0,0 +1,41 @@ + +- · Clarabel jl/rs
GitHub

This code implements the example in the Clarabel "Getting Started" documentation

using Clarabel, SparseArrays, LinearAlgebra
+
+P = sparse([3. 1 -1; 0 4 2; 0 0 5])
+
+q = [1,2,-3.]
3-element Vector{Float64}:
+  1.0
+  2.0
+ -3.0

equality constraint

Aeq = [1. 1. -1.]
+beq = [1.]
1-element Vector{Float64}:
+ 1.0

inequality constraint

Aineq = [0. 1. 0.;
+         0. 0. 1.]
+bineq = [2.,2.]
2-element Vector{Float64}:
+ 2.0
+ 2.0

SOC constraint

Asoc = -I(3)*1.
+bsoc = [0.,0.,0.]
3-element Vector{Float64}:
+ 0.0
+ 0.0
+ 0.0

Clarabel.jl constraint data

A = sparse([Aeq; Aineq; Asoc])
+b = [beq;bineq;bsoc]
+
+cones = [Clarabel.ZeroConeT(1),
+         Clarabel.NonnegativeConeT(2),
+         Clarabel.SecondOrderConeT(3)]
+
+settings = Clarabel.Settings(verbose = true, time_limit = 5)
+
+solver   = Clarabel.Solver()
+
+Clarabel.setup!(solver, P, q, A, b, cones, settings)
+
+solution = Clarabel.solve!(solver)
>>> Clarabel - Results
+Status: SOLVED
+Iterations: 6
+Objective: 2.397
+Solve time:  679μs
+

This page was generated using Literate.jl.

diff --git a/v0.8.0/examples/jl/example_powcone/index.html b/v0.8.0/examples/jl/example_powcone/index.html new file mode 100644 index 0000000..f76c71c --- /dev/null +++ b/v0.8.0/examples/jl/example_powcone/index.html @@ -0,0 +1,85 @@ + +Julia · Clarabel jl/rs
GitHub
using Clarabel, SparseArrays
+
+P = spzeros(6,6)
+
+q = [0., 0., -1., 0., 0., -1.]
+
+A = sparse([
+       -1.  0.  0.  0.  0.  0.;
+        0. -1.  0.  0.  0.  0.;
+        0.  0. -1.  0.  0.  0.;
+        0.  0.  0. -1.  0.  0.;
+        0.  0.  0.  0. -1.  0.;
+        0.  0.  0.  0.  0. -1.;
+        1.  2.  0.  3.  0.  0.;
+        0.  0.  0.  0.  1.  0.])
+
+b = [0., 0., 0., 0., 0., 0., 3., 1.]
+
+cones  = [Clarabel.PowerConeT(0.6), Clarabel.PowerConeT(0.1), Clarabel.ZeroConeT(2)]
+
+solver = Clarabel.Solver()
+
+settings = Clarabel.Settings()
+
+Clarabel.setup!(solver, P, q, A, b, cones, settings)
+
+result = Clarabel.solve!(solver)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 6
+  constraints   = 8
+  nnz(P)        = 0
+  nnz(A)        = 10
+  cones (total) = 3
+    : Zero        = 1,  numel = 2
+    : Power       = 2,  numel = (3,3)
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0   0.0000e+00  -0.0000e+00  0.00e+00  7.43e-01  1.02e+00  1.00e+00  1.00e+00   ------
+  1  -7.2016e-01  -7.0464e-01  1.55e-02  1.57e-01  2.11e-01  2.71e-01  2.63e-01  7.92e-01
+  2  -1.8008e+00  -1.7671e+00  1.90e-02  2.13e-02  2.58e-02  7.82e-02  3.52e-02  9.80e-01
+  3  -1.8433e+00  -1.8426e+00  3.44e-04  5.91e-04  7.02e-04  1.87e-03  9.76e-04  9.80e-01
+  4  -1.8448e+00  -1.8447e+00  7.21e-05  1.27e-04  1.51e-04  3.98e-04  2.09e-04  7.92e-01
+  5  -1.8452e+00  -1.8452e+00  1.52e-05  2.72e-05  3.23e-05  8.48e-05  4.49e-05  7.92e-01
+  6  -1.8453e+00  -1.8453e+00  3.21e-06  5.83e-06  6.92e-06  1.81e-05  9.62e-06  7.92e-01
+  7  -1.8453e+00  -1.8453e+00  6.77e-07  1.25e-06  1.48e-06  3.86e-06  2.06e-06  7.92e-01
+  8  -1.8454e+00  -1.8454e+00  1.43e-07  2.68e-07  3.18e-07  8.23e-07  4.42e-07  7.92e-01
+  9  -1.8454e+00  -1.8454e+00  3.03e-08  5.74e-08  6.81e-08  1.76e-07  9.47e-08  7.92e-01
+ 10  -1.8454e+00  -1.8454e+00  6.41e-09  1.23e-08  1.46e-08  3.75e-08  2.03e-08  7.92e-01
+ 11  -1.8454e+00  -1.8454e+00  1.36e-09  2.64e-09  3.13e-09  8.00e-09  4.35e-09  7.92e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  928μs
>>> Clarabel - Results
+Status: SOLVED
+Iterations: 11
+Objective: -1.845
+Solve time:  928μs
+
result.x
6-element Vector{Float64}:
+ 1.6818451504042895
+ 0.5606011366352672
+ 1.0837601867673565
+ 0.06565085327599281
+ 0.9999999945009342
+ 0.7615949121634987

This page was generated using Literate.jl.

diff --git a/v0.8.0/examples/jl/example_qp/index.html b/v0.8.0/examples/jl/example_qp/index.html new file mode 100644 index 0000000..6346239 --- /dev/null +++ b/v0.8.0/examples/jl/example_qp/index.html @@ -0,0 +1,180 @@ + +Julia · Clarabel jl/rs
GitHub

Quadratic Program (QP) Example in Julia

We will show how to solve the Basic QP example problem both natively in Clarabel.jl and also by solving with Clarabel.jl within either JuMP or Convex.jl.

Clarabel.jl native interface

using Clarabel, SparseArrays
+
+P = sparse([3. 0.;0. 2.].*2)
+
+q = [-1., -4.]
+
+A = sparse([1. -2.;    #<-- LHS of equality constraint
+            1.  0.;    #<-- LHS of inequality constraint (upper bound)
+            0.  1.;    #<-- LHS of inequality constraint (upper bound)
+           -1.  0.;    #<-- LHS of inequality constraint (lower bound)
+            0. -1.;    #<-- LHS of inequality constraint (lower bound)
+            ])
+
+b = [0.;        #<-- RHS of equality constraint
+     ones(4)]   #<-- RHS of inequality constraints
+
+cones =
+    [Clarabel.ZeroConeT(1),           #<--- for the equality constraint
+     Clarabel.NonnegativeConeT(4)]    #<--- for the inequality constraints
+
+settings = Clarabel.Settings()
+
+solver   = Clarabel.Solver()
+
+Clarabel.setup!(solver, P, q, A, b, cones, settings)
+
+result = Clarabel.solve!(solver)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 2
+  constraints   = 5
+  nnz(P)        = 2
+  nnz(A)        = 6
+  cones (total) = 2
+    : Zero        = 1,  numel = 1
+    : Nonnegative = 1,  numel = 4
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0  -3.2878e-01  -1.8973e+01  1.86e+01  9.76e-17  9.02e-17  1.00e+00  1.77e+00   ------
+  1  -5.7453e-01  -1.8040e+00  1.23e+00  4.81e-17  3.23e-17  6.08e-02  1.15e-01  9.44e-01
+  2  -6.4203e-01  -7.5345e-01  1.11e-01  1.63e-17  3.25e-17  5.21e-03  8.97e-03  9.90e-01
+  3  -6.4286e-01  -6.4541e-01  2.55e-03  1.08e-16  3.26e-17  1.19e-04  2.00e-04  9.90e-01
+  4  -6.4286e-01  -6.4288e-01  2.63e-05  4.89e-17  7.99e-18  1.23e-06  2.06e-06  9.90e-01
+  5  -6.4286e-01  -6.4286e-01  2.63e-07  8.82e-15  1.81e-14  1.23e-08  2.06e-08  9.90e-01
+  6  -6.4286e-01  -6.4286e-01  2.63e-09  2.30e-16  4.02e-16  1.23e-10  2.06e-10  9.90e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  614μs
>>> Clarabel - Results
+Status: SOLVED
+Iterations: 6
+Objective: -0.6429
+Solve time:  614μs
+
result.x
2-element Vector{Float64}:
+ 0.4285714281988429
+ 0.2142857140994215

Using JuMP

We can solve the same problem a little more easily by using Clarabel.jl as the backend solver within JuMP. Here is the same problem again:

using Clarabel, JuMP
+
+model = JuMP.Model(Clarabel.Optimizer)
+set_optimizer_attribute(model, "verbose", true)
+
+@variable(model, x[1:2])
+@constraint(model, x[1] == 2x[2])
+@constraint(model,  -1 .<= x .<= 1)
+@objective(model, Min, 3x[1]^2 + 2x[2]^2 - x[1] - 4x[2])
+
+optimize!(model)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 2
+  constraints   = 5
+  nnz(P)        = 2
+  nnz(A)        = 6
+  cones (total) = 2
+    : Zero        = 1,  numel = 1
+    : Nonnegative = 1,  numel = 4
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0  -3.2878e-01  -1.8973e+01  1.86e+01  9.48e-17  1.50e-16  1.00e+00  1.77e+00   ------
+  1  -5.7453e-01  -1.8040e+00  1.23e+00  4.89e-17  6.32e-17  6.08e-02  1.15e-01  9.44e-01
+  2  -6.4203e-01  -7.5345e-01  1.11e-01  5.91e-17  3.34e-17  5.21e-03  8.97e-03  9.90e-01
+  3  -6.4286e-01  -6.4541e-01  2.55e-03  1.14e-16  0.00e+00  1.19e-04  2.00e-04  9.90e-01
+  4  -6.4286e-01  -6.4288e-01  2.63e-05  4.71e-17  3.20e-17  1.23e-06  2.06e-06  9.90e-01
+  5  -6.4286e-01  -6.4286e-01  2.63e-07  8.82e-15  1.81e-14  1.23e-08  2.06e-08  9.90e-01
+  6  -6.4286e-01  -6.4286e-01  2.63e-09  1.96e-16  3.17e-16  1.23e-10  2.06e-10  9.90e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  566μs

Here is the solution

JuMP.value.(x)
2-element Vector{Float64}:
+ 0.4285714281988431
+ 0.21428571409942154

and the solver termination status again

JuMP.termination_status(model)
OPTIMAL::TerminationStatusCode = 1

Using Convex.jl

We can likewise solve the same problem a using Clarabel.jl as the backend solver within Convex.jl. Here is the same problem one more time:

using Clarabel, Convex
+
+x = Variable(2)
+problem = minimize(3square(x[1]) + 2square(x[2]) - x[1] - 4x[2])
+problem.constraints = [x[1] == 2x[2]]
+problem.constraints += [x >= -1; x <= 1]
+solve!(problem, Clarabel.Optimizer; silent_solver = false)
Problem statistics
+  problem is DCP         : true
+  number of variables    : 1 (2 scalar elements)
+  number of constraints  : 3 (5 scalar elements)
+  number of coefficients : 12
+  number of atoms        : 23
+
+Solution summary
+  termination status : OPTIMAL
+  primal status      : FEASIBLE_POINT
+  dual status        : FEASIBLE_POINT
+  objective value    : -0.6429
+
+Expression graph
+  minimize
+   └─ + (convex; real)
+      ├─ * (convex; positive)
+      │  ├─ [3;;]
+      │  └─ qol_elem (convex; positive)
+      │     ├─ …
+      │     └─ …
+      ├─ * (convex; positive)
+      │  ├─ [2;;]
+      │  └─ qol_elem (convex; positive)
+      │     ├─ …
+      │     └─ …
+      ├─ Convex.NegateAtom (affine; real)
+      │  └─ index (affine; real)
+      │     └─ …
+      ⋮
+  subject to
+   ├─ == constraint (affine)
+   │  └─ + (affine; real)
+   │     ├─ index (affine; real)
+   │     │  └─ …
+   │     └─ Convex.NegateAtom (affine; real)
+   │        └─ …
+   ├─ ≥ constraint (affine)
+   │  └─ + (affine; real)
+   │     ├─ 2-element real variable (id: 126…422)
+   │     └─ Convex.NegateAtom (constant; positive)
+   │        └─ …
+   └─ ≤ constraint (affine)
+      └─ + (affine; real)
+         ├─ 2-element real variable (id: 126…422)
+         └─ Convex.NegateAtom (constant; negative)
+            └─ …
+

Here is our solution

evaluate(x)
2-element Vector{Float64}:
+ 0.4285731865024157
+ 0.21428659325133423

and the solver termination status again

problem.status
OPTIMAL::TerminationStatusCode = 1
Warning

Note that in the Clarabel.jl output that follows the call to solve! using Convex.jl, the problem posed to the solver has been converted to a second-order cone program with a linear objective. You can see this because now nnz(P) == 0 (there is no quadratic term in the objective) and the solver reports two second order cone constraints.

Although the solution will be the same, the required number of iterations and solve time are slightly higher. When solving problems with quadratic objectives in Clarabel.jl, it is generally preferable to use either the native Clarabel.jl interface or JuMP, both of which handle quadratic terms in the objective directly.

This page was generated using Literate.jl.

diff --git a/v0.8.0/examples/jl/example_sdp/index.html b/v0.8.0/examples/jl/example_sdp/index.html new file mode 100644 index 0000000..661b1ca --- /dev/null +++ b/v0.8.0/examples/jl/example_sdp/index.html @@ -0,0 +1,129 @@ + +Julia · Clarabel jl/rs
GitHub

Semidefinite Programming (SDP) in Julia

We will show how to solve the Basic QP example problem both natively in Clarabel.jl and also by solving with Clarabel.jl within either JuMP or Convex.jl.

Clarabel.jl native interface

using Clarabel, SparseArrays, LinearAlgebra
+
+n    = 3
+nvec = Int(n*(n+1)/2)
+
+P = spzeros(nvec,nvec)
+
+q = [1.,0.,1.,0.,0.,1.]
+
+A1 = -Diagonal([                         #<-- LHS of SDP constraint
+     1., sqrt(2), 1., sqrt(2), sqrt(2), 1.
+])
+A2 = [1. 2(2.) 3. 2(4.) 2(5.) 6.]        #<-- LHS of equality constraint
+A  = sparse([A1;A2]);
+
+b = [zeros(nvec);                       #<-- RHS of SDP constraint
+     1.]                                #<-- RHS of equality constraint
+
+cones =
+    [Clarabel.PSDTriangleConeT(n),      #<--- for the SDP constraint
+     Clarabel.ZeroConeT(1)]             #<--- for the equality constraints
+
+settings = Clarabel.Settings()
+
+solver   = Clarabel.Solver()
+
+Clarabel.setup!(solver, P, q, A, b, cones, settings)
+
+result = Clarabel.solve!(solver)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 6
+  constraints   = 7
+  nnz(P)        = 0
+  nnz(A)        = 12
+  cones (total) = 2
+    : Zero        = 1,  numel = 1
+    : PSDTriangle = 1,  numel = 6
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0   7.3529e-02   7.3529e-02  2.78e-17  4.30e-01  7.71e-01  1.00e+00  1.33e+00   ------
+  1   1.3789e-01   4.0894e-02  9.70e-02  7.31e-02  1.14e-01  5.93e-03  2.32e-01  8.70e-01
+  2   8.3910e-02   8.1077e-02  2.83e-03  2.57e-03  3.46e-03  6.34e-04  9.67e-03  9.64e-01
+  3   8.6450e-02   8.6422e-02  2.79e-05  2.55e-05  3.38e-05  6.39e-06  9.73e-05  9.90e-01
+  4   8.6475e-02   8.6475e-02  2.79e-07  2.55e-07  3.38e-07  6.39e-08  9.73e-07  9.90e-01
+  5   8.6475e-02   8.6475e-02  2.79e-09  2.55e-09  3.38e-09  6.39e-10  9.73e-09  9.90e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  822μs

Recover the symmetric matrix X

X = zeros(n,n)
+X[triu(ones(Bool,3,3))] .= result.x
+X = Symmetric(X)
3×3 Symmetric{Float64, Matrix{Float64}}:
+ 0.0128947  0.0177209  0.0251946
+ 0.0177209  0.0243534  0.0346243
+ 0.0251946  0.0346243  0.0492269

Using JuMP

We can solve the same problem a little more easily by using Clarabel.jl as the backend solver within JuMP. Here is the same problem again. Note that we are not required to model our SDP constraint in triangular form if we are using JuMP.

using Clarabel, JuMP
+
+n = 3
+A = [1 2 4;
+     2 3 5;
+     4 5 6]
+
+model = JuMP.Model(Clarabel.Optimizer)
+set_optimizer_attribute(model, "verbose", true)
+set_optimizer_attribute(model, "equilibrate_enable",false)
+
+@variable(model, X[1:n,1:n],PSD)
+@constraint(model, tr(A*X) == 1)
+@objective(model, Min, tr(X))
+
+optimize!(model)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 6
+  constraints   = 7
+  nnz(P)        = 0
+  nnz(A)        = 12
+  cones (total) = 2
+    : Zero        = 1,  numel = 1
+    : PSDTriangle = 1,  numel = 6
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: off, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0   7.3529e-02   7.3529e-02  4.16e-17  6.11e-01  3.73e-01  1.00e+00  1.48e+00   ------
+  1   9.5000e-02   4.5267e-02  4.97e-02  7.92e-02  3.07e-02  6.41e-03  1.30e-01  9.46e-01
+  2   8.3793e-02   8.2081e-02  1.71e-03  2.90e-03  1.09e-03  2.10e-04  5.15e-03  9.62e-01
+  3   8.6449e-02   8.6432e-02  1.69e-05  2.88e-05  1.08e-05  2.12e-06  5.18e-05  9.90e-01
+  4   8.6475e-02   8.6475e-02  1.69e-07  2.88e-07  1.08e-07  2.12e-08  5.18e-07  9.90e-01
+  5   8.6475e-02   8.6475e-02  1.69e-09  2.88e-09  1.08e-09  2.12e-10  5.18e-09  9.90e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  793μs

Here is the solution again

JuMP.value.(X)
3×3 Matrix{Float64}:
+ 0.0128947  0.0177209  0.0251946
+ 0.0177209  0.0243534  0.0346243
+ 0.0251946  0.0346243  0.0492269

This page was generated using Literate.jl.

diff --git a/v0.8.0/examples/jl/example_socp/index.html b/v0.8.0/examples/jl/example_socp/index.html new file mode 100644 index 0000000..473fd7a --- /dev/null +++ b/v0.8.0/examples/jl/example_socp/index.html @@ -0,0 +1,147 @@ + +Julia · Clarabel jl/rs
GitHub

SOCP Example in Julia

We will show how to solve this problem both natively in Clarabel.jl and also by solving with Clarabel.jl within JuMP.

Clarabel.jl native interface

using Clarabel, SparseArrays
+
+P = sparse([0. 0.;0. 1.].*2)
+
+q = [0., 0.]
+
+A = sparse([0.  0.
+           -2.  0.;
+            0. -1.])
+b = [ 1.
+     -2.;
+     -2.]
+
+cones = [Clarabel.SecondOrderConeT(3)]
+
+settings = Clarabel.Settings(max_iter = 15, verbose = true)
+
+solver   = Clarabel.Solver()
+
+Clarabel.setup!(solver, P, q, A, b, cones, settings)
+
+result = Clarabel.solve!(solver)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 2
+  constraints   = 3
+  nnz(P)        = 1
+  nnz(A)        = 2
+  cones (total) = 1
+    : SecondOrder = 1,  numel = 3
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 15, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0   4.9292e-01  -1.2888e-01  6.22e-01  1.79e-01  6.48e-17  1.00e+00  2.35e+00   ------
+  1   9.3926e-01   7.9266e-01  1.47e-01  6.38e-03  5.39e-17  4.74e-02  1.60e-01  9.67e-01
+  2   9.9952e-01   9.9654e-01  2.97e-03  6.30e-05  1.07e-16  8.14e-04  2.68e-03  9.90e-01
+  3   1.0000e+00   9.9997e-01  2.98e-05  6.30e-07  1.15e-21  8.16e-06  2.69e-05  9.90e-01
+  4   1.0000e+00   1.0000e+00  2.98e-07  6.30e-09  8.79e-15  8.16e-08  2.69e-07  9.90e-01
+  5   1.0000e+00   1.0000e+00  2.98e-09  6.30e-11  2.13e-16  8.16e-10  2.69e-09  9.90e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  562μs
>>> Clarabel - Results
+Status: SOLVED
+Iterations: 5
+Objective: 1.000
+Solve time:  562μs
+
result.x
2-element Vector{Float64}:
+ 0.9999999999999999
+ 0.9999999997592811

Using JuMP

We can solve the same problem using Clarabel.jl as the backend solver within JuMP. Here is the same problem again:

using Clarabel, JuMP
+
+model = JuMP.Model(Clarabel.Optimizer)
+set_optimizer_attribute(model, "verbose", true)
+
+@variable(model, x[1:2])
+@constraint(model, [1, 2x[1]-2, x[2] - 2] in SecondOrderCone())
+@objective(model, Min, x[2]^2 )
+
+optimize!(model)
-------------------------------------------------------------
+           Clarabel.jl v0.8.0  -  Clever Acronym
+                   (c) Paul Goulart
+                University of Oxford, 2022
+-------------------------------------------------------------
+
+problem:
+  variables     = 2
+  constraints   = 3
+  nnz(P)        = 1
+  nnz(A)        = 2
+  cones (total) = 1
+    : SecondOrder = 1,  numel = 3
+
+settings:
+  linear algebra: direct / qdldl, precision: Float64
+  max iter = 200, time limit = Inf,  max step = 0.990
+  tol_feas = 1.0e-08, tol_gap_abs = 1.0e-08, tol_gap_rel = 1.0e-08,
+  static reg : on, ϵ1 = 1.0e-08, ϵ2 = 4.9e-32
+  dynamic reg: on, ϵ = 1.0e-13, δ = 2.0e-07
+  iter refine: on, reltol = 1.0e-13, abstol = 1.0e-12,
+               max iter = 10, stop ratio = 5.0
+  equilibrate: on, min_scale = 1.0e-04, max_scale = 1.0e+04
+               max iter = 10
+
+iter    pcost        dcost       gap       pres      dres      k/t        μ       step
+---------------------------------------------------------------------------------------------
+  0   4.9292e-01  -1.2888e-01  6.22e-01  1.79e-01  6.48e-17  1.00e+00  2.35e+00   ------
+  1   9.3926e-01   7.9266e-01  1.47e-01  6.38e-03  5.39e-17  4.74e-02  1.60e-01  9.67e-01
+  2   9.9952e-01   9.9654e-01  2.97e-03  6.30e-05  1.07e-16  8.14e-04  2.68e-03  9.90e-01
+  3   1.0000e+00   9.9997e-01  2.98e-05  6.30e-07  1.15e-21  8.16e-06  2.69e-05  9.90e-01
+  4   1.0000e+00   1.0000e+00  2.98e-07  6.30e-09  8.79e-15  8.16e-08  2.69e-07  9.90e-01
+  5   1.0000e+00   1.0000e+00  2.98e-09  6.30e-11  2.13e-16  8.16e-10  2.69e-09  9.90e-01
+---------------------------------------------------------------------------------------------
+Terminated with status = solved
+solve time =  519μs

Here is the solution

JuMP.value.(x)
2-element Vector{Float64}:
+ 0.9999999999999999
+ 0.9999999997592811

and the solver termination status again

JuMP.termination_status(model)
OPTIMAL::TerminationStatusCode = 1

Using Convex.jl

One more time using Clarabel.jl as the backend solver within Convex.jl:

using Clarabel, Convex
+
+x = Variable(2)
+problem = minimize(square(x[2]))
+problem.constraints = [norm([2x[1];x[2]] - [2;2], 2) <= 1]
+solve!(problem, Clarabel.Optimizer; silent_solver = false)
Problem statistics
+  problem is DCP         : true
+  number of variables    : 1 (2 scalar elements)
+  number of constraints  : 1 (1 scalar elements)
+  number of coefficients : 5
+  number of atoms        : 9
+
+Solution summary
+  termination status : OPTIMAL
+  primal status      : FEASIBLE_POINT
+  dual status        : FEASIBLE_POINT
+  objective value    : 1.0
+
+Expression graph
+  minimize
+   └─ qol_elem (convex; positive)
+      ├─ index (affine; real)
+      │  └─ 2-element real variable (id: 806…880)
+      └─ [1.0;;]
+  subject to
+   └─ ≤ constraint (convex)
+      └─ + (convex; real)
+         ├─ norm2 (convex; positive)
+         │  └─ …
+         └─ [-1;;]
+

Here is our solution

evaluate(x)
2-element Vector{Float64}:
+ 1.0
+ 0.9999999973783282

and the solver termination status again

problem.status
OPTIMAL::TerminationStatusCode = 1

This page was generated using Literate.jl.

diff --git a/v0.8.0/examples/py/example_expcone/index.html b/v0.8.0/examples/py/example_expcone/index.html new file mode 100644 index 0000000..446e707 --- /dev/null +++ b/v0.8.0/examples/py/example_expcone/index.html @@ -0,0 +1,34 @@ + +Python · Clarabel jl/rs
GitHub
import clarabel
+import numpy as np
+from scipy import sparse
+
+# Exponential cone example
+# max  x
+# s.t. y * exp(x / y) <= z
+#      y == 1, z == exp(5)
+
+# Define problem data
+P = sparse.csc_matrix((3, 3))
+
+q = np.array([-1., 0., 0.])
+
+A = sparse.csc_matrix(
+    [[-1.,  0.,  0.],
+     [0., -1.,  0.],
+     [0.,  0., -1.],
+     [0.,  1.,  0.],
+     [0.,  0.,  1.]])
+
+b = np.array([0., 0., 0., 1., np.exp(5.)])
+
+cones = [clarabel.ExponentialConeT(), clarabel.ZeroConeT(2)]
+settings = clarabel.DefaultSettings()
+
+solver = clarabel.DefaultSolver(P, q, A, b, cones, settings)
+solver.solve()
+
diff --git a/v0.8.0/examples/py/example_intro/index.html b/v0.8.0/examples/py/example_intro/index.html new file mode 100644 index 0000000..25bbfe8 --- /dev/null +++ b/v0.8.0/examples/py/example_intro/index.html @@ -0,0 +1,50 @@ + +Python "Getting Started" complete example · Clarabel jl/rs
GitHub

Python "Getting Started" complete example

import clarabel
+import numpy as np
+from scipy import sparse
+
+# Define problem data
+P = sparse.csc_matrix(
+        [[3., 1., -1.],
+         [1., 4.,  2.],
+         [-1., 2.,  5.]])
+
+P = sparse.triu(P).tocsc()
+
+q = np.array([1., 2., -3.])
+
+# equality constraint
+Aeq = sparse.csc_matrix([1., 1., -1])
+beq = np.array([1.])
+
+# equality constraint
+Aineq = sparse.csc_matrix(
+        [[0., 1., 0.],
+         [0., 0., 1.]])
+
+bineq = np.array([2., 2.])
+
+# SOC constraint
+Asoc = -sparse.identity(3)
+bsoc = np.array([0., 0., 0.])
+
+# Clarabel constraint data
+A = sparse.vstack([Aeq, Aineq, Asoc]).tocsc()
+b = np.concatenate([beq, bineq, bsoc])
+
+cones = [clarabel.ZeroConeT(1),
+         clarabel.NonnegativeConeT(2),
+         clarabel.SecondOrderConeT(3)]
+
+settings = clarabel.DefaultSettings()
+settings.verbose = True
+settings.time_limit = 5.
+
+solver = clarabel.DefaultSolver(P, q, A, b, cones, settings)
+
+solver.solve()
+
diff --git a/v0.8.0/examples/py/example_powcone/index.html b/v0.8.0/examples/py/example_powcone/index.html new file mode 100644 index 0000000..7f883ef --- /dev/null +++ b/v0.8.0/examples/py/example_powcone/index.html @@ -0,0 +1,37 @@ + +Python · Clarabel jl/rs
GitHub
import clarabel
+import numpy as np
+from scipy import sparse
+
+# Define problem data
+P = sparse.csc_matrix((6, 6))
+
+q = np.array([0., 0., -1., 0., 0., -1.])
+
+A = sparse.csc_matrix(
+    [[-1., 0., 0., 0., 0., 0.],
+     [0., -1., 0., 0., 0., 0.],
+     [0., 0., -1., 0., 0., 0.],
+     [0., 0., 0., -1., 0., 0.],
+     [0., 0., 0., 0., -1., 0.],
+     [0., 0., 0., 0., 0., -1.],
+     [1., 2., 0., 3., 0., 0.],
+     [0., 0., 0., 0., 1., 0.]])
+
+b = np.array([0., 0., 0., 0., 0., 0., 3., 1.])
+
+cones = [
+    clarabel.PowerConeT(0.6),
+    clarabel.PowerConeT(0.1),
+    clarabel.ZeroConeT(2)
+    ]
+
+settings = clarabel.DefaultSettings()
+
+solver = clarabel.DefaultSolver(P, q, A, b, cones, settings)
+solver.solve()
+
diff --git a/v0.8.0/examples/py/example_qp/index.html b/v0.8.0/examples/py/example_qp/index.html new file mode 100644 index 0000000..b1126ad --- /dev/null +++ b/v0.8.0/examples/py/example_qp/index.html @@ -0,0 +1,32 @@ + +Python · Clarabel jl/rs
GitHub
import clarabel
+import numpy as np
+from scipy import sparse
+
+# Define problem data
+P = sparse.csc_matrix([[0., 0.], [0, 0]])
+P = sparse.triu(P).tocsc()
+
+q = np.array([-1., -4.])
+
+A = sparse.csc_matrix(
+    [[1., -2.],        # <-- LHS of equality constraint (lower bound)
+     [1.,  0.],        # <-- LHS of inequality constraint (upper bound)
+     [0.,  1.],        # <-- LHS of inequality constraint (upper bound)
+     [-1.,  0.],       # <-- LHS of inequality constraint (lower bound)
+     [0., -1.]])       # <-- LHS of inequality constraint (lower bound)
+
+b = np.array([0., 1., 1., 1., 1.])
+
+cones = [clarabel.ZeroConeT(1), clarabel.NonnegativeConeT(4)]
+
+settings = clarabel.DefaultSettings()
+
+solver = clarabel.DefaultSolver(P, q, A, b, cones, settings)
+
+solver.solve()
+
diff --git a/v0.8.0/examples/py/example_sdp/index.html b/v0.8.0/examples/py/example_sdp/index.html new file mode 100644 index 0000000..1936654 --- /dev/null +++ b/v0.8.0/examples/py/example_sdp/index.html @@ -0,0 +1,40 @@ + +Python · Clarabel jl/rs
GitHub
import clarabel
+import numpy as np
+from scipy import sparse
+
+
+n = 3
+nvec = int(n*(n+1)/2) 
+
+# Define problem data
+P = sparse.csc_matrix((nvec, nvec))
+P = P.tocsc()
+
+q = np.array([1., 0., 1., 0., 0., 1.])
+sqrt2 = np.sqrt(2.)
+
+A = sparse.csc_matrix(
+    [[-1., 0., 0., 0., 0., 0.],
+     [0., -sqrt2, 0., 0., 0., 0.],
+     [0., 0., -1., 0., 0., 0.],
+     [0., 0., 0., -sqrt2, 0., 0.],
+     [0., 0., 0., 0., -sqrt2, 0.],
+     [0., 0., 0., 0., 0., -1.],
+     [1., 4., 3., 8., 10., 6.]])   
+
+b = np.append(np.zeros(nvec), 1.)
+
+cones = [clarabel.PSDTriangleConeT(n),
+         clarabel.ZeroConeT(1)] 
+
+settings = clarabel.DefaultSettings()
+
+solver = clarabel.DefaultSolver(P, q, A, b, cones, settings)
+
+solver.solve()
+
diff --git a/v0.8.0/examples/py/example_socp/index.html b/v0.8.0/examples/py/example_socp/index.html new file mode 100644 index 0000000..7716d1e --- /dev/null +++ b/v0.8.0/examples/py/example_socp/index.html @@ -0,0 +1,32 @@ + +Python · Clarabel jl/rs
GitHub
import clarabel
+import numpy as np
+from scipy import sparse
+
+# Define problem data
+P = sparse.csc_matrix([[0., 0.], [0., 2.]])
+P = P.tocsc()
+
+q = np.array([0., 0.])
+
+A = sparse.csc_matrix(
+    [[0.,  0.],
+     [-2.,  0.],
+     [0., -1.]])
+
+b = np.array([1., -2., -2.])
+
+cones = [clarabel.SecondOrderConeT(3)]
+
+settings = clarabel.DefaultSettings()
+settings.max_iter = 15
+settings.verbose = True
+
+solver = clarabel.DefaultSolver(P, q, A, b, cones, settings)
+
+solver.solve()
+
diff --git a/v0.8.0/examples/rs/example_expcone/index.html b/v0.8.0/examples/rs/example_expcone/index.html new file mode 100644 index 0000000..d275066 --- /dev/null +++ b/v0.8.0/examples/rs/example_expcone/index.html @@ -0,0 +1,30 @@ + +Rust · Clarabel jl/rs
GitHub

Complete Cargo projects for all Rust examples can be found in examples/rs.

#![allow(non_snake_case)]
+use clarabel::algebra::*;
+use clarabel::solver::*;
+
+fn main() {
+    let P = CscMatrix::zeros((3, 3));
+    let q = vec![-1., 0., 0.];
+
+    let A = CscMatrix::from(&[
+        [-1., 0.,  0.],
+        [0., -1.,  0.],
+        [0.,  0., -1.],
+        [0.,  1.,  0.],
+        [0.,  0.,  1.],
+    ]);
+    let b = vec![0., 0., 0., 1., (5f64).exp()];
+
+    let cones = [ExponentialConeT(), ZeroConeT(2)];
+
+    let settings = DefaultSettings::default();
+    
+    let mut solver = DefaultSolver::new(&P, &q, &A, &b, &cones, settings);
+    solver.solve();
+}
+
diff --git a/v0.8.0/examples/rs/example_powcone/index.html b/v0.8.0/examples/rs/example_powcone/index.html new file mode 100644 index 0000000..47c59e1 --- /dev/null +++ b/v0.8.0/examples/rs/example_powcone/index.html @@ -0,0 +1,37 @@ + +Rust · Clarabel jl/rs
GitHub

Complete Cargo projects for all Rust examples can be found in examples/rs.

#![allow(non_snake_case)]
+use clarabel::algebra::*;
+use clarabel::solver::*;
+
+fn main() {
+    let P = CscMatrix::zeros((6, 6));
+    let q = vec![0., 0., -1., 0., 0., -1.];
+
+    let A = CscMatrix::from(&[
+        [-1., 0., 0., 0., 0., 0.],
+        [0., -1., 0., 0., 0., 0.],
+        [0., 0., -1., 0., 0., 0.],
+        [0., 0., 0., -1., 0., 0.],
+        [0., 0., 0., 0., -1., 0.],
+        [0., 0., 0., 0., 0., -1.],
+        [1., 2., 0., 3., 0., 0.],
+        [0., 0., 0., 0., 1., 0.],
+    ]);
+
+    let b = vec![0., 0., 0., 0., 0., 0., 3., 1.];
+
+    let cones = [PowerConeT(0.6), PowerConeT(0.1), ZeroConeT(2)];
+
+    let settings = DefaultSettings {
+        verbose: true,
+        max_iter: 100,
+        ..DefaultSettings::default()
+    };
+    let mut solver = DefaultSolver::new(&P, &q, &A, &b, &cones, settings);
+    solver.solve();
+}
+
diff --git a/v0.8.0/examples/rs/example_qp/index.html b/v0.8.0/examples/rs/example_qp/index.html new file mode 100644 index 0000000..9f065b2 --- /dev/null +++ b/v0.8.0/examples/rs/example_qp/index.html @@ -0,0 +1,65 @@ + +Rust · Clarabel jl/rs
GitHub

Complete Cargo projects for all Rust examples can be found in examples/rs.

#![allow(non_snake_case)]
+use clarabel::algebra::*;
+use clarabel::solver::*;
+
+fn main() {
+    // QP Example
+
+    // let P = CscMatrix::identity(2);    // For P = I
+    // let P = CscMatrix::zeros((2,2));   // For P = 0
+
+    // direct from sparse data
+    let _P = CscMatrix::new(
+        2,             // m
+        2,             // n
+        vec![0, 1, 2], // colptr
+        vec![0, 1],    // rowval
+        vec![6., 4.],  // nzval
+    );
+
+    // or an easier way for small problems...
+    let P = CscMatrix::from(&[
+        [6., 0.], //
+        [0., 4.], //
+    ]);
+
+    let q = vec![-1., -4.];
+
+    //direct from sparse data
+    let _A = CscMatrix::new(
+        5,                               // m
+        2,                               // n
+        vec![0, 3, 6],                   // colptr
+        vec![0, 1, 3, 0, 2, 4],          // rowval
+        vec![1., 1., -1., -2., 1., -1.], // nzval
+    );
+
+    // or an easier way for small problems...
+    let A = CscMatrix::from(&[
+        [1., -2.], // <-- LHS of equality constraint (lower bound)
+        [1., 0.],  // <-- LHS of inequality constraint (upper bound)
+        [0., 1.],  // <-- LHS of inequality constraint (upper bound)
+        [-1., 0.], // <-- LHS of inequality constraint (lower bound)
+        [0., -1.], // <-- LHS of inequality constraint (lower bound)
+    ]);
+
+    let b = vec![0., 1., 1., 1., 1.];
+
+    let cones = [ZeroConeT(1), NonnegativeConeT(4)];
+
+    let settings = DefaultSettings::default();
+
+    let mut solver = DefaultSolver::new(&P, &q, &A, &b, &cones, settings);
+
+    solver.solve();
+
+    println!("Solution(x)     = {:?}", solver.solution.x);
+    println!("Multipliers (z) = {:?}", solver.solution.z);
+    println!("Slacks (s)      = {:?}", solver.solution.s);
+}
+
diff --git a/v0.8.0/examples/rs/example_sdp/index.html b/v0.8.0/examples/rs/example_sdp/index.html new file mode 100644 index 0000000..f28df88 --- /dev/null +++ b/v0.8.0/examples/rs/example_sdp/index.html @@ -0,0 +1,44 @@ + +Rust · Clarabel jl/rs
GitHub

Complete Cargo projects for all Rust examples can be found in examples/rs.

#![allow(non_snake_case)]
+use clarabel::algebra::*;
+use clarabel::solver::*;
+
+
+fn main() {
+    use clarabel::algebra::*;
+    use clarabel::solver::*;
+
+    let n = 3;
+    let nvec = (n * (n + 1)) >> 1;
+
+    // SDP Example
+    let P = CscMatrix::zeros((nvec, nvec));
+    let c = vec![1., 0., 1., 0., 0., 1.];
+
+    let sqrt2 = 2f64.sqrt();
+    let A = CscMatrix::from(&[
+        [-1., 0., 0., 0., 0., 0.],
+        [0., -sqrt2, 0., 0., 0., 0.],
+        [0., 0., -1., 0., 0., 0.],
+        [0., 0., 0., -sqrt2, 0., 0.],
+        [0., 0., 0., 0., -sqrt2, 0.],
+        [0., 0., 0., 0., 0., -1.],
+        [1., 4., 3., 8., 10., 6.],
+    ]);
+
+    let mut b = vec![0.0; 6];
+    b.push(1.);
+
+    let cones = vec![PSDTriangleConeT(n), ZeroConeT(1)];
+
+    let settings = DefaultSettings::default();
+
+    let mut solver = DefaultSolver::new(&P, &c, &A, &b, &cones, settings);
+
+    solver.solve();
+}
+
diff --git a/v0.8.0/examples/rs/example_socp/index.html b/v0.8.0/examples/rs/example_socp/index.html new file mode 100644 index 0000000..c25c32a --- /dev/null +++ b/v0.8.0/examples/rs/example_socp/index.html @@ -0,0 +1,38 @@ + +Rust · Clarabel jl/rs
GitHub

Complete Cargo projects for all Rust examples can be found in examples/rs.

#![allow(non_snake_case)]
+use clarabel::algebra::*;
+use clarabel::solver::*;
+
+fn main() {
+    // SOCP Example
+
+    let P = CscMatrix::from(&[
+        [0., 0.], //
+        [0., 2.], //
+    ]);
+
+    let q = vec![0., 0.];
+
+    let A = CscMatrix::from(&[
+        [0., 0.],  //
+        [-2., 0.], //
+        [0., -1.], //
+    ]);
+
+    let b = vec![1., -2., -2.];
+
+    let cones = [SecondOrderConeT(3)];
+
+    let settings = DefaultSettings::default();
+
+    let mut solver = DefaultSolver::new(&P, &q, &A, &b, &cones, settings);
+
+    solver.solve();
+
+    println!("Solution = {:?}", solver.solution.x);
+}
+
diff --git a/v0.8.0/index.html b/v0.8.0/index.html new file mode 100644 index 0000000..a4150a5 --- /dev/null +++ b/v0.8.0/index.html @@ -0,0 +1,10 @@ + +Home · Clarabel jl/rs
GitHub

Clarabel is an interior point numerical solver for convex optimization problems using a novel homogeneous embedding. The Clarabel package solves the following problem:

\[\begin{array}{r} +\text{minimize} & \frac{1}{2}x^T P x + q^T x\\[2ex] + \text{subject to} & Ax + s = b \\[1ex] + & s \in \mathcal{K} + \end{array}\]

with decision variables $x \in \mathbb{R}^n$, $s \in \mathbb{R}^m$ and data matrices $P=P^\top \succeq 0$, $q \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. The convex set $\mathcal{K}$ is a composition of convex cones.

Clarabel is available in either a native Julia or a native Rust implementation. Additional language interfaces (Python, C/C++ and R) are available for the Rust version.

Features

  • Versatile: Clarabel solves linear programs (LPs), quadratic programs (QPs), second-order cone programs (SOCPs) and semidefinite programs (SDPs). It also solves problems with exponential, power cone and generalized power cone constraints.
  • Quadratic objectives: Unlike interior point solvers based on the standard homogeneous self-dual embedding (HSDE) model, Clarabel handles quadratic objective without requiring any epigraphical reformulation of its objective function. It can therefore be significantly faster than other HSDE-based solvers for problems with quadratic objective functions.
  • Infeasibility detection: Infeasible problems are detected using using a homogeneous embedding technique.
  • Arbitrary precision types: You can solve problems with any floating point precision, e.g. Float32 or Julia's BigFloat type in Julia and f32 or f64 types in Rust.
  • Open Source: Our code is available on GitHub and distributed under the Apache 2.0 License. The Julia implementation is here. The Rust implementation and Python interface is here.

Credits

The following people are involved in the development of Clarabel:

  • Paul Goulart (main development, maths and algorithms)
  • Yuwen Chen (maths and algorithms)

All contributors are affiliated with the Control Group of the Department of Engineering Science at the University of Oxford.

If this project is useful for your work please consider

License

Clarabel.jl and Clarabel.rs are licensed under the Apache License 2.0 (Julia) : (Rust).

diff --git a/v0.8.0/julia/getting_started_jl/index.html b/v0.8.0/julia/getting_started_jl/index.html new file mode 100644 index 0000000..7776e5f --- /dev/null +++ b/v0.8.0/julia/getting_started_jl/index.html @@ -0,0 +1,127 @@ + +Getting Started · Clarabel jl/rs
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Getting Started

This section describes the process of creating a Clarabel.jl model, populating its settings and problem data, solving the problem and obtaining and understanding results. The description here relates to Clarabel's native API.

The first step is to bring the Clarabel solver and other required packages into scope in your code using:

using Clarabel, SparseArrays, LinearAlgebra

The SparseArrays package from the Julia standard distribution defines the SparseMatrixCSC type for defining matrices in compressed sparse column format.

Problem Format

Clarabel solves optimisation problems in the format:

\[\begin{array}{ll} \text{minimize} & \textstyle{\frac{1}{2}}x^\top Px + q^\top x\\ \text{subject to} & Ax + s = b \\ & s \in \mathcal{K}, \end{array}\]

with decision variables $x \in \mathbb{R}^n$, $s \in \mathbb{R}^m$ and data matrices $P=P^\top \succeq 0$, $q \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. The convex cone $\mathcal{K}$ is a composition of smaller convex cones $\mathcal{K} = \mathcal{K}_1 \times \mathcal{K}_2 \dots \mathcal{K}_p$. Equality conditions can be modelled in this format using the solver's ZeroCone type.

To initialize the solver with an optimisation problem we require three things:

  • The objective function, i.e. the matrix P and the vector q in $\frac{1}{2}x^\top P x + q^\top x$.
  • The data matrix A and vector b, along with a description of the composite cone $\mathcal{K}$ and the dimensions of its constituent pieces.
  • A settings object that specifies how Clarabel solves the problem.

Objective Function

To set the objective function of your optimisation problem simply define the square positive semidefinite matrix $P \in \mathrm{R}^{n\times n}$ and the vector $q \in \mathrm{R}^{n}$.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our objective function is:

\[\begin{equation*} +\min ~ +\frac{1}{2} +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +^T +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +1.0 & 4.0 & 2.0 \\ + -1.0 & 2.0 & 5.0 +\end{array} +\right] +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] ++ +\left[ +\begin{array}{r} +1 \\ 2 \\-3 +\end{array} +\right]^T +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +\end{equation*}\]

Clarabel expects the P matrix to be supplied in Compressed Sparse Column format. P is assumed by the solver to be symmetric and only values in the upper triangular part of P are needed by the solver, i.e. you only need to provide

\[\begin{equation*} +P = +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +⋅ & 4.0 & 2.0 \\ +⋅ & ⋅ & 5.0 +\end{array} +\right] +\end{equation*}\]

The Clarabel default implementation in Julia expects matrix data in sparse SparseMatrixCSC format. We can define our cost data as

P = sparse([3. 1 -1; 0 4 2; 0 0 5])
+q = [1,2,-3.]

Constraints

The Clarabel interface expects constraints to be presented in the single vectorized form $Ax + s = b, s \in \mathcal{K}$, where $\mathcal{K} = \mathcal{K}_1 \times \dots \times \mathcal{K}_p$ and each $\mathcal{K}_i$ is one of the solver's supported cone types.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our constraints are:

  • A single equality constraint $x_1 + x_2 - x_3 = 1$.
  • A pair of inequalities such that $x_2$ and $x_3$ are each less than 2.
  • A second order cone constraint on the 3-dimensional vector $x$.

For the three constraints above, we have

\[ +\begin{align*} + +A_{eq} &= +\left[ +\begin{array}{lll} +1 & 1 & -1 +\end{array} +\right], +\quad & +b_{eq} &= +\left[ +\begin{array}{l} +1 +\end{array} +\right], + +\\[4ex] + +A_{ineq} &= +\left[ +\begin{array}{lll} +0 & 1 & 0 \\ +0 & 0 & 1 +\end{array} +\right], +\quad & +b_{ineq} &= +\left[ +\begin{array}{l} +2\\2 +\end{array} +\right], + +\\[4ex] + +A_{soc} &= +\left[ +\begin{array}{rrr} +-1 & 0 & 0 \\ + 0 & -1 & 0 \\ + 0 & 0 & -1 +\end{array} +\right], +\quad & +b_{soc} &= +\left[ +\begin{array}{l} +0 \\0 \\0 +\end{array} +\right] + +\end{align*} +\]

We can then define our constraint data as

using SparseArrays
+
+# equality constraint
+Aeq = [1. 1. -1.]
+beq = [1.]
+
+# inequality constraint
+Aineq = [0. 1. 0.;
+         0. 0. 1.]
+bineq = [2.,2.]
+
+# SOC constraint
+Asoc = -I(3)*1.
+bsoc = [0.,0.,0.]
+
+# Clarabel.jl constraint data
+A = sparse([Aeq; Aineq; Asoc])
+b = [beq;bineq;bsoc]

Clarabel.jl expects to receive a vector of cone specifications. For the above constraints we should also define

# Clarabel.jl cone specification
+cones = [Clarabel.ZeroConeT(1), Clarabel.NonnegativeConeT(2), Clarabel.SecondOrderConeT(3)]

There is no restriction on the ordering of the cones that appear in cones, nor on the number of instances of each type that appear. The cones should be of type Vector{Clarabel.SupportedCone}, and your input vector b should be compatible with the sum of the cone dimensions.

Note

Note carefully the signs in the above example. The inequality condition is $A_{ineq} x \le b_{ineq}$, which is equivalent to $A_{ineq} x + s = b_{ineq}$ with $s \ge 0$, i.e. $s$ in the Nonnegative cone. The SOC condition is $x \in \mathcal{K}_{SOC}$, or equivalently $-x + s = 0$ with $s \in \mathcal{K}_{SOC}$.

Solver Settings

Solver settings are stored in a Settings object and can be modified by the user. To create a Settings object just call the constructor:

settings = Clarabel.Settings()

To adjust those values, you can pass options and parameters as a key-value pair to the constructor or edit the corresponding field afterwards. For example, if you want to disable verbose printing and set a 5 second time limit on the solver, you can use

settings = Clarabel.Settings(verbose = false, time_limit = 5)
+
+# the following is equivalent
+settings = Clarabel.Settings()
+settings.verbose    = false
+settings.time_limit = 5

The full set of user configurable solver settings are listed in the API Reference.

Making a Solver

The problem data, user settings and workspace variables are all stored in a top level Solver type. First define an empty Solver:

solver  = Clarabel.Solver()

Then provide the solver with problem data using

Clarabel.setup!(solver, P, q, A, b, cones, settings)

This takes an internal copy of all data parameters and initializes internal variables and other objects in the solver. The final settings argument is optional.

Now you can solve your problem using:

solution = Clarabel.solve!(solver)
+solution.x   # primal solution
+solution.z   # dual solution
+solution.s   # slacks

Results

Once the solver algorithm terminates you can inspect the solution using the solution object. The outcome of the solve is specified in solution.status and will be one of the following :

Status Codes

Status CodeDescription
SOLVEDSolver terminated with a solution.
PRIMAL_INFEASIBLEProblem is primal infeasible. Solution returned is a certificate of primal infeasibility.
DUAL_INFEASIBLEProblem is dual infeasible. Solution returned is a certificate of dual infeasibility.
ALMOST_SOLVEDSolver terminated with a solution (reduced accuracy).
ALMOST_PRIMAL_INFEASIBLEProblem is primal infeasible. Solution returned is a certificate of primal infeasibility (reduced accuracy).
ALMOST_DUAL_INFEASIBLEProblem is dual infeasible. Solution returned is a certificate of dual infeasibility (reduced accuracy).
MAX_ITERATIONSIteration limit reached before solution or infeasibility certificate found.
MAX_TIMETime limit reached before solution or infeasibility certificate found.
NUMERICAL_ERRORSolver terminated with a numerical error.
INSUFFICIENT_PROGRESSSolver terminated due to lack of progress.

The total solution time (include combined setup! and solve! times) is given in solution.solve_time. Detailed information about the solve time and memory allocation can be found in the solver's timer field.

Warning

Be careful to retrieve solver solutions from the solution that is returned by the solver, or directly from a solver object from the solver.solution field. Do not use the solver.variables, since these have both homogenization and equilibration scaling applied and therefore do not solve the optimization problem posed to the solver.

diff --git a/v0.8.0/julia/installation_jl/index.html b/v0.8.0/julia/installation_jl/index.html new file mode 100644 index 0000000..d831310 --- /dev/null +++ b/v0.8.0/julia/installation_jl/index.html @@ -0,0 +1,6 @@ + +Installation · Clarabel jl/rs
GitHub

Installation

Clarabel.jl can be installed using the Julia package manager for Julia v1.0 and higher. Inside the Julia REPL, type ] to enter the Pkg REPL mode then run

pkg> add Clarabel

If you want to install the latest version from the github repository run

pkg> add Clarabel#main

diff --git a/v0.8.0/julia/jump/index.html b/v0.8.0/julia/jump/index.html new file mode 100644 index 0000000..dfbb7a8 --- /dev/null +++ b/v0.8.0/julia/jump/index.html @@ -0,0 +1,8 @@ + +JuMP Interface · Clarabel jl/rs
GitHub

JuMP Interface

Clarabel.jl implements support for MathOptInterface, and is therefore compatible with JuMP. This allows you to describe and modify your optimisation problem with JuMP and use Clarabel.jl as the backend solver.

Setting Clarabel.jl Backend

To specify Clarabel.jl as the solver for your JuMP model, load the solver module with using Clarabel and then configure Clarabel as the solver backend when initialising the JuMP model:

model = JuMP.Model(Clarabel.Optimizer)

Solver Settings

Solver-specific settings can be passed after the Clarabel.Optimizer object. For example, if you want to adjust the maximum number of iterations and turn off verbose printing use

set_optimizer_attribute(model, "verbose", true)
+set_optimizer_attribute(model, "max_iter", 25)

The full list of available settings can be found in the Settings section of the API Reference.

Results

After solving the problem the result can be obtained using the standard JuMP commands. To see if the optimisation was successful use

JuMP.termination_status(model)
+JuMP.primal_status(model)

If a solution is available, the optimal objective value can be retrieved using

JuMP.objective_value(model)

and the value of a decision variable x can be obtained with

JuMP.value.(x)

For more information on JuMP, see the JuMP documentation.

diff --git a/v0.8.0/julia/linear_solvers/index.html b/v0.8.0/julia/linear_solvers/index.html new file mode 100644 index 0000000..a23c60c --- /dev/null +++ b/v0.8.0/julia/linear_solvers/index.html @@ -0,0 +1,6 @@ + +Linear Solvers · Clarabel jl/rs
GitHub

Linear System Solvers

The primary numerical operation inside Clarabel.jl is the solution of a symmetric quasidefinite linear system at each iteration. The solver currently supports three different solvers to perform factorization and forward/backward substitution on this system.

The linear solver can be configured in Settings using the direct_solve_method field, e.g.

settings = Solver.Settings(direct_solve_method = :qdldl)

The solvers currently supported are

SymbolPackageDescription
:qdldlQDLDL.jlDefault solver
:mklPardiso.jlIntel MKL Pardiso
:panuaPardiso.jlPanua Pardiso
:ma57HSL.jlHSL MA57
:cholmodJulia native ldlt solverSuiteSparse.CHOLMOD
Note

To use the Pardiso solvers you must install the respective libraries and the corresponding Julia wrapper. For more information about installing these, visit the Pardiso.jl repository page. You must also bring Pardiso into scope first (i.e. using Pardiso) before solving. The same is true for the HSL MA57 solver, which requires the HSL library and the Julia wrapper [HSL.jl].

QDLDL is a single threaded solver written in pure Julia, and is generally adequate for problems of small to medium size.

diff --git a/v0.8.0/literate/arbitrary_precision.jl b/v0.8.0/literate/arbitrary_precision.jl new file mode 100644 index 0000000..66d189a --- /dev/null +++ b/v0.8.0/literate/arbitrary_precision.jl @@ -0,0 +1,72 @@ +#= +# Arbitrary Precision Arithmetic + +Clarabel.jl supports the use of arbitrary precision floating-point types, including Julia's `BigFloat` type. To use this feature you must specify all of your problem data using a common floating point type and explictly create Clarabel.Solver and (optional) Clarabel.Settings objects of the the same type. + +Start by creating the solver and settings with the desired precision: +=# + +using Clarabel, LinearAlgebra, SparseArrays + +settings = Clarabel.Settings{BigFloat}( + verbose = true, + direct_kkt_solver = true, + direct_solve_method = :qdldl) + +solver = Clarabel.Solver{BigFloat}() + +#= +### Objective and constraint data + +We next put the objective function into the standard Clarabel.jl form. Here we use the same problem data as in the [QP Example](@ref), but in `BigFloat` format : +=# + +P = sparse(BigFloat[3. 0.;0. 2.].*2) +q = BigFloat[-1., -4.] +A = sparse( + BigFloat[1. -2.; #<-- LHS of equality constraint + 1. 0.; #<-- LHS of inequality constraint (upper bound) + 0. 1.; #<-- LHS of inequality constraint (upper bound) + -1. 0.; #<-- LHS of inequality constraint (lower bound) + 0. -1.; #<-- LHS of inequality constraint (lower bound) + ]) +b = [zero(BigFloat); #<-- RHS of equality constraint + ones(BigFloat,4) #<-- RHS of inequality constraints + ] + +cones = + [Clarabel.ZeroConeT(1), #<--- for the equality constraint + Clarabel.NonnegativeConeT(4)] #<--- for the inequality constraints + +nothing #hide + +# You can optionally set the global precision of Julia's BigFloat type before solving +setprecision(BigFloat,128) +nothing #hide + +# Finally we can set up the problem in the usual way and solve + +Clarabel.setup!(solver, P, q, A, b, cones, settings) +result = Clarabel.solve!(solver) + +#then retrieve the solution + +result.x + +# Notice that the above would fail if the default solver was used, because Clarabel.jl uses Float64 by default +Clarabel.Solver() + +#= +!!! warning + For arbitrary precision arithmetic using `BigFloat` types you must select an internal linear solver + within Clarabel.jl that supports it. We recommend that you use the [QDLDL.jl](https://github.com/osqp/QDLDL.jl) package for such problems, + and configure it as the linear solver by setting both `direct_kkt_solver = true` and `direct_solve_method = :qdldl` in the Settings object. + +## With Convex.jl / JuMP + +Clarabel.jl also supports arbitrary precision arithmetic through Convex.jl. See the example in the [Convex.jl Interface](@ref) section. + + +!!! note + `JuMP` does not currently support arbitrary precision. However, if you want to use `Clarabel` directly with `MathOptInterface`, you can use: `Clarabel.Optimizer{<: AbstractFloat}` as your optimizer. As above, the problem data precision of your MathOptInterface-model must agree with the optimizer's precision. +=# diff --git a/v0.8.0/literate/build/arbitrary_precision/index.html b/v0.8.0/literate/build/arbitrary_precision/index.html new file mode 100644 index 0000000..790ae61 --- /dev/null +++ b/v0.8.0/literate/build/arbitrary_precision/index.html @@ -0,0 +1,37 @@ + +Arbitrary Precision Arithmetic · Clarabel jl/rs
GitHub

Arbitrary Precision Arithmetic

Clarabel.jl supports the use of arbitrary precision floating-point types, including Julia's BigFloat type. To use this feature you must specify all of your problem data using a common floating point type and explictly create Clarabel.Solver and (optional) Clarabel.Settings objects of the the same type.

Start by creating the solver and settings with the desired precision:

using Clarabel, LinearAlgebra, SparseArrays
+
+settings = Clarabel.Settings{BigFloat}(
+            verbose = true,
+            direct_kkt_solver = true,
+            direct_solve_method = :qdldl)
+
+solver   = Clarabel.Solver{BigFloat}()
Clarabel model with Float precision: BigFloat
+

Objective and constraint data

We next put the objective function into the standard Clarabel.jl form. Here we use the same problem data as in the QP Example, but in BigFloat format :

P = sparse(BigFloat[3. 0.;0. 2.].*2)
+q = BigFloat[-1., -4.]
+A = sparse(
+    BigFloat[1. -2.;    #<-- LHS of equality constraint
+             1.  0.;    #<-- LHS of inequality constraint (upper bound)
+             0.  1.;    #<-- LHS of inequality constraint (upper bound)
+            -1.  0.;    #<-- LHS of inequality constraint (lower bound)
+             0. -1.;    #<-- LHS of inequality constraint (lower bound)
+    ])
+b = [zero(BigFloat);    #<-- RHS of equality constraint
+     ones(BigFloat,4)   #<-- RHS of inequality constraints
+    ]
+
+cones =
+    [Clarabel.ZeroConeT(1),           #<--- for the equality constraint
+     Clarabel.NonnegativeConeT(4)]    #<--- for the inequality constraints

You can optionally set the global precision of Julia's BigFloat type before solving

setprecision(BigFloat,128)

Finally we can set up the problem in the usual way and solve

Clarabel.setup!(solver, P, q, A, b, cones, settings)
+result = Clarabel.solve!(solver)
+
+#then retrieve the solution
+
+result.x
2-element Vector{BigFloat}:
+ 0.4285714281988430338225782293218456073824
+ 0.2142857140994215319229440884193854024541

Notice that the above would fail if the default solver was used, because Clarabel.jl uses Float64 by default

Clarabel.Solver()
Clarabel model with Float precision: Float64
+
Warning

For arbitrary precision arithmetic using BigFloat types you must select an internal linear solver within Clarabel.jl that supports it. We recommend that you use the QDLDL.jl package for such problems, and configure it as the linear solver by setting both direct_kkt_solver = true and direct_solve_method = :qdldl in the Settings object.

With Convex.jl / JuMP

Clarabel.jl also supports arbitrary precision arithmetic through Convex.jl. See the example in the Convex.jl Interface section.

Note

JuMP does not currently support arbitrary precision. However, if you want to use Clarabel directly with MathOptInterface, you can use: Clarabel.Optimizer{<: AbstractFloat} as your optimizer. As above, the problem data precision of your MathOptInterface-model must agree with the optimizer's precision.

This page was generated using Literate.jl.

diff --git a/v0.8.0/literate/build/convex_jl/index.html b/v0.8.0/literate/build/convex_jl/index.html new file mode 100644 index 0000000..89029f5 --- /dev/null +++ b/v0.8.0/literate/build/convex_jl/index.html @@ -0,0 +1,61 @@ + +Convex.jl Interface · Clarabel jl/rs
GitHub

Convex.jl Interface

Clarabel.jl implements support for MathOptInterface, and is therefore compatible with Convex.jl. This allows you to describe and modify your optimisation problem with Convex.jl and use Clarabel as the backend solver.

Setting Clarabel.jl Backend

You should construct your problem in the usual way in Convex.jl, and then solve using Clarabel.Optimizer, i.e. by calling solve! with

solve!(problem, Clarabel.Optimizer)

where problem is an object of type Convex.Problem.

Convex.jl or JuMP?

Clarabel.jl supports both Convex.jl and JuMP via MathOptInterface. Both packages are excellent and can make problem construction considerably easier than via the solver's native interface.

For problems with quadratic objective functions, JuMP is generally preferred when using Clarabel.jl since it will keep the quadratic function in the objective rather than reformulating the problem to a form with a linear cost and additional second-order cone constraints. Clarabel.jl natively supports quadratic objectives and solve times are generally faster if this reformulation is avoided.

Arbitrary Precision Arithmetic

Clarabel.jl supports arbitrary precision arithmetic for Convex.jl. Here is the QP Example implemented using BigFloat types.

#hide setprecision(BigFloat,256)
+using Clarabel, Convex
+
+x = Variable(2)
+objective = 3square(x[1]) + 2square(x[2]) - x[1] - 4x[2]
+problem = minimize(objective; numeric_type = BigFloat)
+problem.constraints = [x[1] == 2x[2]]
+problem.constraints += [x >= -1; x <= 1]
+solve!(problem, Clarabel.Optimizer{BigFloat}; silent_solver = false)
Problem statistics
+  problem is DCP         : true
+  number of variables    : 1 (2 scalar elements)
+  number of constraints  : 3 (5 scalar elements)
+  number of coefficients : 12
+  number of atoms        : 23
+
+Solution summary
+  termination status : OPTIMAL
+  primal status      : FEASIBLE_POINT
+  dual status        : FEASIBLE_POINT
+  objective value    : -0.6428999999999999999999999999999999999998
+
+Expression graph
+  minimize
+   └─ + (convex; real)
+      ├─ * (convex; positive)
+      │  ├─ [3;;]
+      │  └─ qol_elem (convex; positive)
+      │     ├─ …
+      │     └─ …
+      ├─ * (convex; positive)
+      │  ├─ [2;;]
+      │  └─ qol_elem (convex; positive)
+      │     ├─ …
+      │     └─ …
+      ├─ Convex.NegateAtom (affine; real)
+      │  └─ index (affine; real)
+      │     └─ …
+      ⋮
+  subject to
+   ├─ == constraint (affine)
+   │  └─ + (affine; real)
+   │     ├─ index (affine; real)
+   │     │  └─ …
+   │     └─ Convex.NegateAtom (affine; real)
+   │        └─ …
+   ├─ ≥ constraint (affine)
+   │  └─ + (affine; real)
+   │     ├─ 2-element real variable (id: 900…815)
+   │     └─ Convex.NegateAtom (constant; positive)
+   │        └─ …
+   └─ ≤ constraint (affine)
+      └─ + (affine; real)
+         ├─ 2-element real variable (id: 900…815)
+         └─ Convex.NegateAtom (constant; negative)
+            └─ …
+

This page was generated using Literate.jl.

diff --git a/v0.8.0/literate/convex_jl.jl b/v0.8.0/literate/convex_jl.jl new file mode 100644 index 0000000..670f618 --- /dev/null +++ b/v0.8.0/literate/convex_jl.jl @@ -0,0 +1,33 @@ +#= +# Convex.jl Interface +Clarabel.jl implements support for [MathOptInterface](https://jump.dev/JuMP.jl/stable/moi/), and is therefore compatible with [Convex.jl](https://jump.dev/Convex.jl/stable/). This allows you to describe and modify your optimisation problem with Convex.jl and use Clarabel as the backend solver. + +## Setting Clarabel.jl Backend + +You should construct your problem in the usual way in Convex.jl, and then solve using `Clarabel.Optimizer`, i.e. by calling `solve!` with +```julia +solve!(problem, Clarabel.Optimizer) +``` +where `problem` is an object of type `Convex.Problem`. + +## Convex.jl or JuMP? + +Clarabel.jl supports both Convex.jl and JuMP via MathOptInterface. Both packages are excellent and can make problem construction considerably easier than via the solver's native interface. + +For problems with quadratic objective functions, JuMP is generally preferred when using Clarabel.jl since it will keep the quadratic function in the objective rather than reformulating the problem to a form with a linear cost and additional second-order cone constraints. Clarabel.jl natively supports quadratic objectives and solve times are generally faster if this reformulation is avoided. + +## Arbitrary Precision Arithmetic + +Clarabel.jl supports arbitrary precision arithmetic for Convex.jl. Here is the [QP Example](@ref) implemented using `BigFloat` types. + +=# + +#hide setprecision(BigFloat,256) +using Clarabel, Convex + +x = Variable(2) +objective = 3square(x[1]) + 2square(x[2]) - x[1] - 4x[2] +problem = minimize(objective; numeric_type = BigFloat) +problem.constraints = [x[1] == 2x[2]] +problem.constraints += [x >= -1; x <= 1] +solve!(problem, Clarabel.Optimizer{BigFloat}; silent_solver = false) diff --git a/v0.8.0/method/index.html b/v0.8.0/method/index.html new file mode 100644 index 0000000..9428965 --- /dev/null +++ b/v0.8.0/method/index.html @@ -0,0 +1,6 @@ + +- · Clarabel jl/rs
GitHub
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GitHub

Getting Started

This section describes the process of creating a Clarabel model directly in Python, populating its settings and problem data, solving the problem and obtaining and understanding results. The complete example from this page can be found here.

The first step is to bring the Clarabel solver and other required packages into scope in your code using:

import clarabel
+import numpy as np
+from scipy import sparse

Problem Format

Clarabel solves optimisation problems in the format:

\[\begin{array}{ll} \text{minimize} & \textstyle{\frac{1}{2}}x^\top Px + q^\top x\\ \text{subject to} & Ax + s = b \\ & s \in \mathcal{K}, \end{array}\]

with decision variables $x \in \mathbb{R}^n$, $s \in \mathbb{R}^m$ and data matrices $P=P^\top \succeq 0$, $q \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. The convex cone $\mathcal{K}$ is a composition of smaller convex cones $\mathcal{K} = \mathcal{K}_1 \times \mathcal{K}_2 \dots \mathcal{K}_p$. Equality conditions can be modelled in this format using the solver's ZeroCone type.

To initialize the solver with an optimisation problem we require three things:

  • The objective function, i.e. the matrix P and the vector q in $\frac{1}{2}x^\top P x + q^\top x$.
  • The data matrix A and vector b, along with a description of the composite cone $\mathcal{K}$ and the dimensions of its constituent pieces.
  • A settings object that specifies how Clarabel solves the problem.

Objective Function

To set the objective function of your optimisation problem simply define the square positive semidefinite matrix $P \in \mathrm{R}^{n\times n}$ and the vector $q \in \mathrm{R}^{n}$.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our objective function is:

\[\begin{equation*} +\min ~ +\frac{1}{2} +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +^T +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +1.0 & 4.0 & 2.0 \\ + -1.0 & 2.0 & 5.0 +\end{array} +\right] +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] ++ +\left[ +\begin{array}{r} +1 \\ 2 \\-3 +\end{array} +\right]^T +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +\end{equation*}\]

Clarabel expects the P matrix to be supplied in Compressed Sparse Column format. P is assumed by the solver to be symmetric and only values in the upper triangular part of P are needed by the solver, i.e. you only need to provide

\[\begin{equation*} +P = +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +⋅ & 4.0 & 2.0 \\ +⋅ & ⋅ & 5.0 +\end{array} +\right] +\end{equation*}\]

The Clarabel default implementation in Python expects matrix data in Compressed Sparse Column format as produced by scipy. We can define our cost data as

P = sparse.csc_matrix(
+        [[ 3., 1., -1.],
+         [ 1., 4.,  2.],
+         [-1., 2.,  5.]])
+
+P = sparse.triu(P).tocsc()
+
+q = np.array([1., 2., -3.])
+
+

Constraints

The Clarabel interface expects constraints to be presented in the single vectorized form $Ax + s = b, s \in \mathcal{K}$, where $\mathcal{K} = \mathcal{K}_1 \times \dots \times \mathcal{K}_p$ and each $\mathcal{K}_i$ is one of the solver's supported cone types.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our constraints are:

  • A single equality constraint $x_1 + x_2 - x_3 = 1$.
  • A pair of inequalities such that $x_2$ and $x_3$ are each less than 2.
  • A second order cone constraint on the 3-dimensional vector $x$.

For the three constraints above, we have

\[ +\begin{align*} + +A_{eq} &= +\left[ +\begin{array}{lll} +1 & 1 & -1 +\end{array} +\right], +\quad & +b_{eq} &= +\left[ +\begin{array}{l} +1 +\end{array} +\right], + +\\[4ex] + +A_{ineq} &= +\left[ +\begin{array}{lll} +0 & 1 & 0 \\ +0 & 0 & 1 +\end{array} +\right], +\quad & +b_{ineq} &= +\left[ +\begin{array}{l} +2\\2 +\end{array} +\right], + +\\[4ex] + +A_{soc} &= +\left[ +\begin{array}{rrr} +-1 & 0 & 0 \\ + 0 & -1 & 0 \\ + 0 & 0 & -1 +\end{array} +\right], +\quad & +b_{soc} &= +\left[ +\begin{array}{l} +0 \\0 \\0 +\end{array} +\right] + +\end{align*} +\]

We can define our constraint data as

# equality constraint
+Aeq = sparse.csc_matrix([1.,1.,-1])
+
+beq = np.array([1.])
+
+# equality constraint
+Aineq = sparse.csc_matrix(
+        [[0., 1., 0.],
+         [0., 0., 1.]])
+
+bineq = np.array([2.,2.])
+
+# SOC constraint
+Asoc = -sparse.identity(3)
+
+bsoc = np.array([0.,0.,0.])
+
+# Clarabel constraint data
+A = sparse.vstack([Aeq,Aineq,Asoc]).tocsc()
+
+b = np.concatenate([beq,bineq,bsoc])

Clarabel expects to receive a vector of cone specifications. For the above constraints we should also define

cones = [clarabel.ZeroConeT(1),
+         clarabel.NonnegativeConeT(2),
+         clarabel.SecondOrderConeT(3)]

There is no restriction on the ordering of the cones that appear in cones, nor on the number of instances of each type that appear. Your input vector b should be compatible with the sum of the cone dimensions.

Note

Note carefully the signs in the above example. The inequality condition is $A_{ineq} x \le b_{ineq}$, which is equivalent to $A_{ineq} x + s = b_{ineq}$ with $s \ge 0$, i.e. $s$ in the Nonnegative cone. The SOC condition is $x \in \mathcal{K}_{SOC}$, or equivalently $-x + s = 0$ with $s \in \mathcal{K}_{SOC}$.

Solver Settings

Solver settings for the Clarabel's default implementation in Rust are stored in a PyDefaultSettings object and can be modified by the user. To create a settings object using all defaults you can call the constructor directly:

settings = clarabel.DefaultSettings()

If you want to disable verbose printing and set a 5 second time limit on the solver, you can then just modify the fields:

settings.verbose = False
+settings.time_limit = 5.

The Clarabel Python interface set supports the same options as those listed in the Rust API Reference.

Making a Solver

Finally, populate the solver with problem data and solve:

solver = clarabel.DefaultSolver(P,q,A,b,cones,settings)
+
+solution = solver.solve()
+solution.x  # primal solution
+solution.z  # dual solution
+solution.s  # primal slacks

Results

The outcome of the solve is specified in solver.solution.status and will be one of the following :

Status CodeDescription
UnsolvedDefault value, only occurs prior to calling solve
SolvedSolution found
PrimalInfeasibleProblem is primal infeasible
DualInfeasibleProblem is dual infeasible
AlmostSolvedSolution found (reduced accuracy)
AlmostPrimalInfeasibleProblem is primal infeasible (reduced accuracy)
AlmostDualInfeasibleProblem is dual infeasible (reduced accuracy)
MaxIterationsSolver halted after reaching iteration limit
MaxTimeSolver halted after reaching time limit
NumericalErrorSolver terminated with a numerical error
InsufficientProgressSolver terminated due to lack of progress

The total solution time is available in solution.solve_time.

CVXPY Interface

The same problem above can also be modelled in CVXPY and solved via Clarabel.

import cvxpy as cp
+
+P = [[3., 1., -1.],
+     [1., 4.,  2.],
+     [-1., 2.,  5.]]
+
+q = [1., 2., -3.]
+
+# Create optimization variables
+x = cp.Variable(3)
+
+# Create two
+constraints = [x[0] + x[1] - x[2] == 1,
+               x[1] <= 2,
+               x[2] <= 2,
+               cp.SOC(x[0], x[1:])]
+
+# Form objective.
+obj = cp.Minimize(0.5*cp.quad_form(x, P) + q @ x)
+
+# Form and solve problem.
+prob = cp.Problem(obj, constraints)
+prob.solve(solver='CLARABEL', verbose=True)
+
diff --git a/v0.8.0/python/installation_py/index.html b/v0.8.0/python/installation_py/index.html new file mode 100644 index 0000000..3768801 --- /dev/null +++ b/v0.8.0/python/installation_py/index.html @@ -0,0 +1,8 @@ + +Installation · Clarabel jl/rs
GitHub

Installation

The Clarabel Python interface supports version 3.7 or newer. To install directly, use:

pip install clarabel

Installing from source

You can also download and build the repository directly from Github. You will need to have a working Rust installation to compile the Python interface.

To obtain the source: 

git clone https://github.com/oxfordcontrol/Clarabel.rs
+cd Clarabel.rs

The Python interface to the Rust solver is implemented using PyO3 and can be built with Maturin. First create and activate a python virtual environment for your build:

python3 -m venv .env
+source .env/bin/activate

Install maturin in your virtual environment:

pip install maturin

Then compile the Rust source with PyO3 bindings enabled:

maturin develop --release

To check that Clarabel works within the virtual environment, you can then run

python examples/python/example_qp.py

To compile and install the solver outside of the virtual environment, at the last step you can instead run

maturin build -i python --release --features python

inside the virtual environment to produce a .whl. Then outside the virtual environment run

python3 -m pip install <.whl-file-you-just-built>
diff --git a/v0.8.0/rust/getting_started_rs/index.html b/v0.8.0/rust/getting_started_rs/index.html new file mode 100644 index 0000000..e5eab3b --- /dev/null +++ b/v0.8.0/rust/getting_started_rs/index.html @@ -0,0 +1,145 @@ + +Getting Started · Clarabel jl/rs
GitHub

Getting Started

This section describes the process of creating a Clarabel.rs model, populating its settings and problem data, solving the problem and obtaining and understanding results. It is assumed here that you are building your project using cargo.

Full documentation for the Rust API is available in the API Reference.

The first step is to make the Clarabel solver a dependency in your project by adding:

[dependencies]
+clarabel = {version = "0"}

to your project's Cargo.toml file. Then bring the solver into scope in your source files:

use clarabel::algebra::*;
+use clarabel::solver::*;

The algebra module defines the CscMatrix type for defining matrices in compressed sparse column format. It also contains some basic utilities for creating and manipulating sparse matrices.

Problem Format

Clarabel solves optimisation problems in the format:

\[\begin{array}{ll} \text{minimize} & \textstyle{\frac{1}{2}}x^\top Px + q^\top x\\ \text{subject to} & Ax + s = b \\ & s \in \mathcal{K}, \end{array}\]

with decision variables $x \in \mathbb{R}^n$, $s \in \mathbb{R}^m$ and data matrices $P=P^\top \succeq 0$, $q \in \mathbb{R}^n$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$. The convex cone $\mathcal{K}$ is a composition of smaller convex cones $\mathcal{K} = \mathcal{K}_1 \times \mathcal{K}_2 \dots \mathcal{K}_p$. Equality conditions can be modelled in this format using the solver's ZeroCone type.

To initialize the solver with an optimisation problem we require three things:

  • The objective function, i.e. the matrix P and the vector q in $\frac{1}{2}x^\top P x + q^\top x$.
  • The data matrix A and vector b, along with a description of the composite cone $\mathcal{K}$ and the dimensions of its constituent pieces.
  • A settings object that specifies how Clarabel solves the problem.

Objective Function

To set the objective function of your optimisation problem simply define the square positive semidefinite matrix $P \in \mathrm{R}^{n\times n}$ and the vector $q \in \mathrm{R}^{n}$.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our objective function is:

\[\begin{equation*} +\min ~ +\frac{1}{2} +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +^T +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +1.0 & 4.0 & 2.0 \\ + -1.0 & 2.0 & 5.0 +\end{array} +\right] +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] ++ +\left[ +\begin{array}{r} +1 \\ 2 \\-3 +\end{array} +\right]^T +\left[ +\begin{array}{l} +x_1 \\ x_2 \\x_3 +\end{array} +\right] +\end{equation*}\]

Clarabel expects the P matrix to be supplied in Compressed Sparse Column format. P is assumed by the solver to be symmetric and only values in the upper triangular part of P are needed by the solver, i.e. you only need to provide

\[\begin{equation*} +P = +\left[ +\begin{array}{rrr} +3.0 & 1.0 & -1.0 \\ +⋅ & 4.0 & 2.0 \\ +⋅ & ⋅ & 5.0 +\end{array} +\right] +\end{equation*}\]

The Clarabel default implementation in Rust expects matrix data as a CscMatrix object and provides a set of basic utilities for sparse matrix construction. We can define our cost data as

let P = CscMatrix::new(
+    3,                             // m
+    3,                             // n
+    vec![0, 1, 3, 6],              // colptr
+    vec![0, 0, 1, 0, 1, 2],        // rowval
+    vec![3., 1., 4., -1., 2., 5.], // nzval
+);
+
+let q = vec![1., 2., -3.];
Tip

To specify P = I, you can use

let P = CscMatrix::identity(2);

where in this case we have had to be specific about the floating point data type we want. To use a zero matrix (e.g. if solving an LP), you can use

let P = CscMatrix::spalloc((2,2),0);

to construct a sparse matrix with no entries.

The solver will not conduct any check on the internal correctness of matrices passed in CscMatrix format. You can do this externally using the check_format method, e.g.:

assert!(P.check_format().is_ok());

Constraints

The Clarabel interface expects constraints to be presented in the single vectorized form $Ax + s = b, s \in \mathcal{K}$, where $\mathcal{K} = \mathcal{K}_1 \times \dots \times \mathcal{K}_p$ and each $\mathcal{K}_i$ is one of the solver's supported cone types.

Suppose that we have a problem with decision variable $x \in \mathbb{R}^3$ and our constraints are:

  • A single equality constraint $x_1 + x_2 - x_3 = 1$.
  • A pair of inequalities such that $x_2$ and $x_3$ are each less than 2.
  • A second order cone constraint on the 3-dimensional vector $x$.

For the three constraints above, we have

\[ +\begin{align*} + +A_{eq} &= +\left[ +\begin{array}{lll} +1 & 1 & -1 +\end{array} +\right], +\quad & +b_{eq} &= +\left[ +\begin{array}{l} +1 +\end{array} +\right], + +\\[4ex] + +A_{ineq} &= +\left[ +\begin{array}{lll} +0 & 1 & 0 \\ +0 & 0 & 1 +\end{array} +\right], +\quad & +b_{ineq} &= +\left[ +\begin{array}{l} +2\\2 +\end{array} +\right], + +\\[4ex] + +A_{soc} &= +\left[ +\begin{array}{rrr} +-1 & 0 & 0 \\ + 0 & -1 & 0 \\ + 0 & 0 & -1 +\end{array} +\right], +\quad & +b_{soc} &= +\left[ +\begin{array}{l} +0 \\0 \\0 +\end{array} +\right] + +\end{align*} +\]

We can define our constraint data as

let Aeq = CscMatrix::new(
+        1,                 // m
+        3,                 // n
+        vec![0, 1, 2, 3],  // colptr
+        vec![0, 0, 0],     // rowval
+        vec![1., 1., -1.], // nzval
+    );
+
+    let Aineq = CscMatrix::new(
+        2,                // m
+        3,                // n
+        vec![0, 0, 1, 2], // colptr
+        vec![0, 1],       // rowval
+        vec![1., 1.],     // nzval
+    );
+
+    let mut Asoc = CscMatrix::identity(3);
+    Asoc.negate();
+
+    let A = CscMatrix::vcat(&Aeq, &Aineq);
+    let A = CscMatrix::vcat(&A, &Asoc);
+
+    let b = vec![1., 2., 2., 0., 0., 0.];
+
+    // optional correctness check 
+    assert!(A.check_format().is_ok());

Clarabel.rs expects to receive a vector of cone specifications. For the above constraints we should also define

# Clarabel.jl cone specification
+let cones = [ZeroConeT(1), NonnegativeConeT(2), SecondOrderConeT(3)];

There is no restriction on the ordering of the cones that appear in cones, nor on the number of instances of each type that appear. Your input vector b should be compatible with the sum of the cone dimensions.

Note

Note carefully the signs in the above example. The inequality condition is $A_{ineq} x \le b_{ineq}$, which is equivalent to $A_{ineq} x + s = b_{ineq}$ with $s \ge 0$, i.e. $s$ in the Nonnegative cone. The SOC condition is $x \in \mathcal{K}_{SOC}$, or equivalently $-x + s = 0$ with $s \in \mathcal{K}_{SOC}$.

Solver Settings

Solver settings for the Clarabel's default implementation in Rust are stored in a DefaultSettings object and can be modified by the user. To create a settings object using all defaults you can call the constructor directly:

let settings = DefaultSettings::default();

Alternatively, you can use the DefaultSettingsBuilder to specify custom settings. For example, if you want to disable verbose printing and set a 5 second time limit on the solver, you can use:

let settings = DefaultSettingsBuilder::default()
+    .verbose(false)
+    .time_limit(1.)
+    .build()
+    .unwrap();

The full set of user configurable solver settings are listed in the Rust API Reference.

Making a Solver

Finally populate the solver with problem data and solve:

let mut solver = DefaultSolver::new(&P, &q, &A, &b, &cones, settings);
+
+solver.solve();

Results

Once the solver algorithm terminates you can inspect the solution using the solution field of the solver. 

println!("Solution status = {:?}", solver.solution.status);
+println!("Primal solution = {:?}", solver.solution.x);
+println!("Dual solution   = {:?}", solver.solution.z);
+println!("Primal slacks   = {:?}", solver.solution.s);

The outcome of the solve is specified in solver.solution.status and will be one of the following :

Status CodeDescription
UnsolvedDefault value, only occurs prior to calling solve
SolvedSolution found
PrimalInfeasibleProblem is primal infeasible
DualInfeasibleProblem is dual infeasible
AlmostSolvedSolution found (reduced accuracy)
AlmostPrimalInfeasibleProblem is primal infeasible (reduced accuracy)
AlmostDualInfeasibleProblem is dual infeasible (reduced accuracy)
MaxIterationsSolver halted after reaching iteration limit
MaxTimeSolver halted after reaching time limit
NumericalErrorSolver terminated with a numerical error
InsufficientProgressSolver terminated due to lack of progress

The total solution time is available in solver.solution.solve_time.

Warning

Be careful to retrieve solver solutions from the solution that is returned by the solver, or directly from a solver object from the solver.solution field. Do not use the solver.variables, since these have both homogenization and equilibration scaling applied and therefore do not solve the optimization problem posed to the solver.

diff --git a/v0.8.0/rust/installation_rs/index.html b/v0.8.0/rust/installation_rs/index.html new file mode 100644 index 0000000..38328b6 --- /dev/null +++ b/v0.8.0/rust/installation_rs/index.html @@ -0,0 +1,9 @@ + +Installation · Clarabel jl/rs
GitHub

Installation

Using Cargo

Clarabel.rs is available through the Rust registry at crates.io and can be imported directly as a dependency in your project. Just add

[dependencies]
+clarabel = "0"

in your project's Cargo.toml file to obtain the latest version.

Direct from source

You can also download and build the repository directly from Github: 

git clone https://github.com/oxfordcontrol/Clarabel.rs
+cd Clarabel.rs
+cargo build --release

To check that your installation worked, you can run

cargo run --example qp
diff --git a/v0.8.0/search_index.js b/v0.8.0/search_index.js new file mode 100644 index 0000000..7cfccc8 --- /dev/null +++ b/v0.8.0/search_index.js @@ -0,0 +1,3 @@ +var documenterSearchIndex = {"docs": +[{"location":"api_rs/#api-ref-rust","page":"Rust API ⧉","title":"Rust API Reference","text":"","category":"section"},{"location":"api_rs/","page":"Rust API ⧉","title":"Rust API ⧉","text":" \n Old Page\n \n \n \n \n

Clarabel.rs API documentation is at https://docs.rs/clarabel/. Trying to redirect you...

\n ","category":"page"},{"location":"python/getting_started_py/#Getting-Started","page":"Getting Started","title":"Getting Started","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"This section describes the process of creating a Clarabel model directly in Python, populating its settings and problem data, solving the problem and obtaining and understanding results. The complete example from this page can be found here.","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"The first step is to bring the Clarabel solver and other required packages into scope in your code using:","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"import clarabel\nimport numpy as np\nfrom scipy import sparse","category":"page"},{"location":"python/getting_started_py/#Problem-Format","page":"Getting Started","title":"Problem Format","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_problem.md\",\n plaintext = true)","category":"page"},{"location":"python/getting_started_py/#Objective-Function","page":"Getting Started","title":"Objective Function","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_objective.md\",\n plaintext = true)","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"The Clarabel default implementation in Python expects matrix data in Compressed Sparse Column format as produced by scipy. We can define our cost data as","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"P = sparse.csc_matrix(\n [[ 3., 1., -1.],\n [ 1., 4., 2.],\n [-1., 2., 5.]])\n\nP = sparse.triu(P).tocsc()\n\nq = np.array([1., 2., -3.])\n\n","category":"page"},{"location":"python/getting_started_py/#Constraints","page":"Getting Started","title":"Constraints","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_constraints.md\",\n plaintext = true)","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"We can define our constraint data as","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"# equality constraint\nAeq = sparse.csc_matrix([1.,1.,-1])\n\nbeq = np.array([1.])\n\n# equality constraint\nAineq = sparse.csc_matrix(\n [[0., 1., 0.],\n [0., 0., 1.]])\n\nbineq = np.array([2.,2.])\n\n# SOC constraint\nAsoc = -sparse.identity(3)\n\nbsoc = np.array([0.,0.,0.])\n\n# Clarabel constraint data\nA = sparse.vstack([Aeq,Aineq,Asoc]).tocsc()\n\nb = np.concatenate([beq,bineq,bsoc])","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"Clarabel expects to receive a vector of cone specifications. For the above constraints we should also define","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"cones = [clarabel.ZeroConeT(1),\n clarabel.NonnegativeConeT(2),\n clarabel.SecondOrderConeT(3)]","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"There is no restriction on the ordering of the cones that appear in cones, nor on the number of instances of each type that appear. Your input vector b should be compatible with the sum of the cone dimensions.","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_constraints_note.md\",\n plaintext = true)","category":"page"},{"location":"python/getting_started_py/#Solver-Settings","page":"Getting Started","title":"Solver Settings","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"Solver settings for the Clarabel's default implementation in Rust are stored in a PyDefaultSettings object and can be modified by the user. To create a settings object using all defaults you can call the constructor directly:","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"settings = clarabel.DefaultSettings()","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"If you want to disable verbose printing and set a 5 second time limit on the solver, you can then just modify the fields:","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"settings.verbose = False\nsettings.time_limit = 5.","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"The Clarabel Python interface set supports the same options as those listed in the Rust API Reference.","category":"page"},{"location":"python/getting_started_py/#Making-a-Solver","page":"Getting Started","title":"Making a Solver","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"Finally, populate the solver with problem data and solve:","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"solver = clarabel.DefaultSolver(P,q,A,b,cones,settings)\n\nsolution = solver.solve()\nsolution.x # primal solution\nsolution.z # dual solution\nsolution.s # primal slacks","category":"page"},{"location":"python/getting_started_py/#Results","page":"Getting Started","title":"Results","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"The outcome of the solve is specified in solver.solution.status and will be one of the following :","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"Status Code Description\nUnsolved Default value, only occurs prior to calling solve\nSolved Solution found\nPrimalInfeasible Problem is primal infeasible\nDualInfeasible Problem is dual infeasible\nAlmostSolved Solution found (reduced accuracy)\nAlmostPrimalInfeasible Problem is primal infeasible (reduced accuracy)\nAlmostDualInfeasible Problem is dual infeasible (reduced accuracy)\nMaxIterations Solver halted after reaching iteration limit\nMaxTime Solver halted after reaching time limit\nNumericalError Solver terminated with a numerical error\nInsufficientProgress Solver terminated due to lack of progress","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"The total solution time is available in solution.solve_time. ","category":"page"},{"location":"python/getting_started_py/#CVXPY-Interface","page":"Getting Started","title":"CVXPY Interface","text":"","category":"section"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"The same problem above can also be modelled in CVXPY and solved via Clarabel.","category":"page"},{"location":"python/getting_started_py/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_intro_cvxpy.py\",\n language = :python)","category":"page"},{"location":"examples/example_expcone/#Exponential-Cone-Example","page":"Problem Description","title":"Exponential Cone Example","text":"","category":"section"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"In this example we show how to model optimization problems with exponential cone constraints. The exponential cone is defined as ","category":"page"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"beginaligned\nmathcalK_exp = (x y z) mid y geq 0 ye^xy le z cup \n (xyz) mid x leq 0 y = 0 z geq 0 \nendaligned","category":"page"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"We will solve the following optimization problem:","category":"page"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"beginarrayll textmaximize x2ex\ntextsubject to \nbeginarrayrl\ny e^x y lez \ny =1 \nz =e^5\nendarray\nendarray","category":"page"},{"location":"examples/example_expcone/#Objective-function","page":"Problem Description","title":"Objective function","text":"","category":"section"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"The Clarabel solver's default configuration expects problems to be posed as minimization problems, so we define:","category":"page"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"P = 0\ntextrmand\nq = -\nbeginbmatrix 1 0 0\nendbmatrix^T","category":"page"},{"location":"examples/example_expcone/#Constraints","page":"Problem Description","title":"Constraints","text":"","category":"section"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"The solver's default configuration expects constraints in the form Ax + s = b, where s is in a cone or composition of cones. In this case we can write ","category":"page"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"beginbmatrix 0 0 0\nendbmatrix\n - I\nbeginbmatrix x y z \nendbmatrix = s\nin mathcalK_exp","category":"page"},{"location":"examples/example_expcone/","page":"Problem Description","title":"Problem Description","text":"and then append the two additional equality constraints.","category":"page"},{"location":"examples/py/example_intro/#python_example_intro_complete","page":"Python \"Getting Started\" complete example","title":"Python \"Getting Started\" complete example","text":"","category":"section"},{"location":"examples/py/example_intro/","page":"Python \"Getting Started\" complete example","title":"Python \"Getting Started\" complete example","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_intro.py\",\n language = :python)","category":"page"},{"location":"examples/py/example_sdp/","page":"Python","title":"Python","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_sdp.py\",\n language = :python)","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"EditURL = \"../arbitrary_precision.jl\"","category":"page"},{"location":"literate/build/arbitrary_precision/#Arbitrary-Precision-Arithmetic","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"","category":"section"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Clarabel.jl supports the use of arbitrary precision floating-point types, including Julia's BigFloat type. To use this feature you must specify all of your problem data using a common floating point type and explictly create Clarabel.Solver and (optional) Clarabel.Settings objects of the the same type.","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Start by creating the solver and settings with the desired precision:","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"using Clarabel, LinearAlgebra, SparseArrays\n\nsettings = Clarabel.Settings{BigFloat}(\n verbose = true,\n direct_kkt_solver = true,\n direct_solve_method = :qdldl)\n\nsolver = Clarabel.Solver{BigFloat}()","category":"page"},{"location":"literate/build/arbitrary_precision/#Objective-and-constraint-data","page":"Arbitrary Precision Arithmetic","title":"Objective and constraint data","text":"","category":"section"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"We next put the objective function into the standard Clarabel.jl form. Here we use the same problem data as in the QP Example, but in BigFloat format :","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"P = sparse(BigFloat[3. 0.;0. 2.].*2)\nq = BigFloat[-1., -4.]\nA = sparse(\n BigFloat[1. -2.; #<-- LHS of equality constraint\n 1. 0.; #<-- LHS of inequality constraint (upper bound)\n 0. 1.; #<-- LHS of inequality constraint (upper bound)\n -1. 0.; #<-- LHS of inequality constraint (lower bound)\n 0. -1.; #<-- LHS of inequality constraint (lower bound)\n ])\nb = [zero(BigFloat); #<-- RHS of equality constraint\n ones(BigFloat,4) #<-- RHS of inequality constraints\n ]\n\ncones =\n [Clarabel.ZeroConeT(1), #<--- for the equality constraint\n Clarabel.NonnegativeConeT(4)] #<--- for the inequality constraints\n\nnothing #hide","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"You can optionally set the global precision of Julia's BigFloat type before solving","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"setprecision(BigFloat,128)\nnothing #hide","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Finally we can set up the problem in the usual way and solve","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Clarabel.setup!(solver, P, q, A, b, cones, settings)\nresult = Clarabel.solve!(solver)\n\n#then retrieve the solution\n\nresult.x","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Notice that the above would fail if the default solver was used, because Clarabel.jl uses Float64 by default","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Clarabel.Solver()","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"warning: Warning\nFor arbitrary precision arithmetic using BigFloat types you must select an internal linear solver within Clarabel.jl that supports it. We recommend that you use the QDLDL.jl package for such problems, and configure it as the linear solver by setting both direct_kkt_solver = true and direct_solve_method = :qdldl in the Settings object.","category":"page"},{"location":"literate/build/arbitrary_precision/#With-Convex.jl-/-JuMP","page":"Arbitrary Precision Arithmetic","title":"With Convex.jl / JuMP","text":"","category":"section"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"Clarabel.jl also supports arbitrary precision arithmetic through Convex.jl. See the example in the Convex.jl Interface section.","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"note: Note\nJuMP does not currently support arbitrary precision. However, if you want to use Clarabel directly with MathOptInterface, you can use: Clarabel.Optimizer{<: AbstractFloat} as your optimizer. As above, the problem data precision of your MathOptInterface-model must agree with the optimizer's precision.","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"","category":"page"},{"location":"literate/build/arbitrary_precision/","page":"Arbitrary Precision Arithmetic","title":"Arbitrary Precision Arithmetic","text":"This page was generated using Literate.jl.","category":"page"},{"location":"_common/getting_started_constraints_note/","page":"-","title":"-","text":"note: Note\nNote carefully the signs in the above example. The inequality condition is A_ineq x le b_ineq, which is equivalent to A_ineq x + s = b_ineq with s ge 0, i.e. s in the Nonnegative cone. The SOC condition is x in mathcalK_SOC, or equivalently -x + s = 0 with s in mathcalK_SOC.","category":"page"},{"location":"user_guide_c_cpp/#user-guide-r","page":"C/C++","title":"C/C++ Installation and User Guide","text":"","category":"section"},{"location":"user_guide_c_cpp/","page":"C/C++","title":"C/C++","text":"C and C++ interfaces to Clarabel can be found here.","category":"page"},{"location":"user_guide_c_cpp/","page":"C/C++","title":"C/C++","text":"The C++ version accepts solver inputs in the form of Eigen matrices and vectors. ","category":"page"},{"location":"examples/example_powcone/#Power-Cone-Example","page":"Problem Description","title":"Power Cone Example","text":"","category":"section"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"In this example we show how to model optimization problems with 3-dimensional power cone constraints. The power cone is defined as ","category":"page"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"mathcalK_pow(alpha) = (x y z) mid x^alpha y^(1-alpha) \ngeq z (xy) geq 0 ","category":"page"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"with alpha in (01).","category":"page"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"We will solve the following optimization problem:","category":"page"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"beginarrayll textmaximize x_1^06 y^04 + x_2^012ex\ntextsubject to \nbeginarrayrl\n(x_1 y x_2) ge 0 \nx_1 + 2y + 3x_2 = 3\nendarray\nendarray","category":"page"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"which is equivalent to","category":"page"},{"location":"examples/example_powcone/","page":"Problem Description","title":"Problem Description","text":"beginarrayll textmaximize z_1 + z_22ex\ntextsubject to \nbeginarrayrl\n(x1 y z1) inmathcalK_pow(06) \n(x2 1 z2) inmathcalK_pow(01) \nx_1 + 2y + 3x_2 =3\nendarray\nendarray","category":"page"},{"location":"examples/py/example_powcone/","page":"Python","title":"Python","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_powcone.py\",\n language = :python)","category":"page"},{"location":"julia/linear_solvers/#Linear-System-Solvers","page":"Linear Solvers","title":"Linear System Solvers","text":"","category":"section"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"The primary numerical operation inside Clarabel.jl is the solution of a symmetric quasidefinite linear system at each iteration. The solver currently supports three different solvers to perform factorization and forward/backward substitution on this system.","category":"page"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"The linear solver can be configured in Settings using the direct_solve_method field, e.g.","category":"page"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"settings = Solver.Settings(direct_solve_method = :qdldl)","category":"page"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"The solvers currently supported are","category":"page"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"Symbol Package Description\n:qdldl QDLDL.jl Default solver\n:mkl Pardiso.jl Intel MKL Pardiso\n:panua Pardiso.jl Panua Pardiso\n:ma57 HSL.jl HSL MA57\n:cholmod Julia native ldlt solver SuiteSparse.CHOLMOD","category":"page"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"note: Note\nTo use the Pardiso solvers you must install the respective libraries and the corresponding Julia wrapper. For more information about installing these, visit the Pardiso.jl repository page. You must also bring Pardiso into scope first (i.e. using Pardiso) before solving. The same is true for the HSL MA57 solver, which requires the HSL library and the Julia wrapper [HSL.jl].","category":"page"},{"location":"julia/linear_solvers/","page":"Linear Solvers","title":"Linear Solvers","text":"QDLDL is a single threaded solver written in pure Julia, and is generally adequate for problems of small to medium size. ","category":"page"},{"location":"examples/example_sdp/#Semidefinite-Program-(SDP)-Example","page":"Problem Description","title":"Semidefinite Program (SDP) Example","text":"","category":"section"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"In this example we show how to model semidefinite programming problems, i.e. problems defined with constraints on the symmetric positive semidefinite cone.","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"Given some symmetric matrix X in mathbbR^ntimes n, Clarabel takes only the upper triangular vector of n(n+1)2 entries when imposing semidefinite constraints. For example, given a 3 times 3 symmetric matrix variable ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"X = beginbmatrix\nx_1 x_2 x_4 \nx_2 x_3 x_5 \nx_4 x_5 x_6\nendbmatrix","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"we would take as our decision variable the 6 element vector ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"x = \nbeginbmatrix\nx_1 x_2 x_3 x_4 x_5 x_6\nendbmatrix","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"We define an operation ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"textrmvec(X) = \nbeginbmatrix\nx_1 sqrt2x_2 x_3 sqrt2x_4 sqrt2x_5 x_6\nendbmatrix","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"on symmetric matrices such that inner products are preserved, i.e. textrmtr(AB) = textrmvec(A)^Ttextrmvec(B), and will use the relationship ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"S in mathbbR^n quad Longleftrightarrow quad textrmvec(S) in mathcalK_texttri^n","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"where mathcalK_texttri^n is the positive semidefinite triangle cone.","category":"page"},{"location":"examples/example_sdp/#Problem-statement","page":"Problem Description","title":"Problem statement","text":"","category":"section"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"We will solve the following optimization problem:","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"beginarrayll textminimize textrmtrace(X)2ex\ntextsubject to \nbegingathered\nlangle AXrangle = 1 \nX succeq 0\nendgathered\nendarray","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"where X = X^T inmathbbR^3times 3 and the symmetric matrix A is defined as ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"A = beginbmatrix\n1 2 4 \n2 3 5 \n4 5 6\nendbmatrix","category":"page"},{"location":"examples/example_sdp/#Objective-function","page":"Problem Description","title":"Objective function","text":"","category":"section"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"We can model the trace of the matrix X by defining our objective function as ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"frac12x^TPx + q^Tx ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"with P = 0 and q = beginbmatrix 1 0 1 0 0 1 endbmatrix^T, where the elements of q are chosen to select those elements of x corresonding to the diagonal of the matrix X. ","category":"page"},{"location":"examples/example_sdp/#Constraints","page":"Problem Description","title":"Constraints","text":"","category":"section"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"The solver's default configuration expects constraints in the form Ax + s = b. In this we can write our semidefiniteness constraint as ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"-textvec(X) = s in mathcalK_texttri^n","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"where mathcalK_texttri^n is the cone of vectors representing the triangular part of matrices in mathbbS_+^n.","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"For the equality constraint can we must be careful to rewrite the inner product on X in a form that is an equivalent linear function of x. We therefore write ","category":"page"},{"location":"examples/example_sdp/","page":"Problem Description","title":"Problem Description","text":"beginaligned\n langle AXrangle = textrmvec(A)^Ttextrmvec(X) \n = beginbmatrix\n1 (2cdot 2) 3 (2cdot 4) (2cdot 5) 6\nendbmatrix\nbeginbmatrix\nx_1 x_2 x_3 x_4 x_5 x_6\nendbmatrix = 1\nendaligned","category":"page"},{"location":"examples/example_socp/#SOCP-Example","page":"Problem Description","title":"SOCP Example","text":"","category":"section"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"Suppose that we want to solve the following 2-dimensional optimization problem:","category":"page"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"beginarrayll textminimize x_2^22ex\ntextsubject to leftbeginpmatrix 2x_1 x_2 endpmatrix\n- beginpmatrix 2 2 endpmatrixright_2 le 1\nendarray","category":"page"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"We will show how to solve this problem through each of Clarabel's supported languages and interfaces.","category":"page"},{"location":"examples/example_socp/#Objective-function","page":"Problem Description","title":"Objective function","text":"","category":"section"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"The Clarabel solver's default configuration expects problem data in the form frac12x^top P x + q^top x. We therefore define the objective function data as","category":"page"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"P = 2 cdot beginbmatrix 0 0 0 1endbmatrix\ntextrmand\nq = beginbmatrix 0 0endbmatrix","category":"page"},{"location":"examples/example_socp/#Constraints","page":"Problem Description","title":"Constraints","text":"","category":"section"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"The solver's default configuration expects constraints in the form Ax + s = b, where s in mathcalK for some composite cone mathcalK. We have a single constraint on the 2-norm of a vector, so we rewrite","category":"page"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"leftbeginpmatrix 2x_1 x_2 endpmatrix - beginpmatrix 2 2 endpmatrixright_2 le 1\nquad Longleftrightarrow quad\nbeginpmatrix 1 2x_1 - 2 x_2 - 2 endpmatrix in mathcalK_SOC","category":"page"},{"location":"examples/example_socp/","page":"Problem Description","title":"Problem Description","text":"which puts our constraint in the form b - Ax in mathcalK_SOC. ","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"EditURL = \"../../../../examples/jl/example_intro.jl\"","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"This code implements the example in the Clarabel \"Getting Started\" documentation","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"using Clarabel, SparseArrays, LinearAlgebra\n\nP = sparse([3. 1 -1; 0 4 2; 0 0 5])\n\nq = [1,2,-3.]","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"equality constraint","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"Aeq = [1. 1. -1.]\nbeq = [1.]","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"inequality constraint","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"Aineq = [0. 1. 0.;\n 0. 0. 1.]\nbineq = [2.,2.]","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"SOC constraint","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"Asoc = -I(3)*1.\nbsoc = [0.,0.,0.]","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"Clarabel.jl constraint data","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"A = sparse([Aeq; Aineq; Asoc])\nb = [beq;bineq;bsoc]\n\ncones = [Clarabel.ZeroConeT(1),\n Clarabel.NonnegativeConeT(2),\n Clarabel.SecondOrderConeT(3)]\n\nsettings = Clarabel.Settings(verbose = true, time_limit = 5)\n\nsolver = Clarabel.Solver()\n\nClarabel.setup!(solver, P, q, A, b, cones, settings)\n\nsolution = Clarabel.solve!(solver)","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"","category":"page"},{"location":"examples/jl/example_intro/","page":"-","title":"-","text":"This page was generated using Literate.jl.","category":"page"},{"location":"rust/getting_started_rs/#Getting-Started","page":"Getting Started","title":"Getting Started","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"This section describes the process of creating a Clarabel.rs model, populating its settings and problem data, solving the problem and obtaining and understanding results. It is assumed here that you are building your project using cargo.","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Full documentation for the Rust API is available in the API Reference.","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"The first step is to make the Clarabel solver a dependency in your project by adding:","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"[dependencies]\nclarabel = {version = \"0\"}","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"to your project's Cargo.toml file. Then bring the solver into scope in your source files:","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"use clarabel::algebra::*;\nuse clarabel::solver::*;","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"The algebra module defines the CscMatrix type for defining matrices in compressed sparse column format. It also contains some basic utilities for creating and manipulating sparse matrices.","category":"page"},{"location":"rust/getting_started_rs/#Problem-Format","page":"Getting Started","title":"Problem Format","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_problem.md\",\n plaintext = true)","category":"page"},{"location":"rust/getting_started_rs/#Objective-Function","page":"Getting Started","title":"Objective Function","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_objective.md\",\n plaintext = true)","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"The Clarabel default implementation in Rust expects matrix data as a CscMatrix object and provides a set of basic utilities for sparse matrix construction. We can define our cost data as","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"let P = CscMatrix::new(\n 3, // m\n 3, // n\n vec![0, 1, 3, 6], // colptr\n vec![0, 0, 1, 0, 1, 2], // rowval\n vec![3., 1., 4., -1., 2., 5.], // nzval\n);\n\nlet q = vec![1., 2., -3.];","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"tip: Tip\nTo specify P = I, you can uselet P = CscMatrix::identity(2);where in this case we have had to be specific about the floating point data type we want. To use a zero matrix (e.g. if solving an LP), you can uselet P = CscMatrix::spalloc((2,2),0);to construct a sparse matrix with no entries.The solver will not conduct any check on the internal correctness of matrices passed in CscMatrix format. You can do this externally using the check_format method, e.g.:assert!(P.check_format().is_ok());","category":"page"},{"location":"rust/getting_started_rs/#Constraints","page":"Getting Started","title":"Constraints","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_constraints.md\",\n plaintext = true)","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"We can define our constraint data as","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"let Aeq = CscMatrix::new(\n 1, // m\n 3, // n\n vec![0, 1, 2, 3], // colptr\n vec![0, 0, 0], // rowval\n vec![1., 1., -1.], // nzval\n );\n\n let Aineq = CscMatrix::new(\n 2, // m\n 3, // n\n vec![0, 0, 1, 2], // colptr\n vec![0, 1], // rowval\n vec![1., 1.], // nzval\n );\n\n let mut Asoc = CscMatrix::identity(3);\n Asoc.negate();\n\n let A = CscMatrix::vcat(&Aeq, &Aineq);\n let A = CscMatrix::vcat(&A, &Asoc);\n\n let b = vec![1., 2., 2., 0., 0., 0.];\n\n // optional correctness check \n assert!(A.check_format().is_ok());","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Clarabel.rs expects to receive a vector of cone specifications. For the above constraints we should also define","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"# Clarabel.jl cone specification\nlet cones = [ZeroConeT(1), NonnegativeConeT(2), SecondOrderConeT(3)];","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"There is no restriction on the ordering of the cones that appear in cones, nor on the number of instances of each type that appear. Your input vector b should be compatible with the sum of the cone dimensions.","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_constraints_note.md\",\n plaintext = true)","category":"page"},{"location":"rust/getting_started_rs/#Solver-Settings","page":"Getting Started","title":"Solver Settings","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Solver settings for the Clarabel's default implementation in Rust are stored in a DefaultSettings object and can be modified by the user. To create a settings object using all defaults you can call the constructor directly:","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"let settings = DefaultSettings::default();","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Alternatively, you can use the DefaultSettingsBuilder to specify custom settings. For example, if you want to disable verbose printing and set a 5 second time limit on the solver, you can use:","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"let settings = DefaultSettingsBuilder::default()\n .verbose(false)\n .time_limit(1.)\n .build()\n .unwrap();","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"The full set of user configurable solver settings are listed in the Rust API Reference.","category":"page"},{"location":"rust/getting_started_rs/#Making-a-Solver","page":"Getting Started","title":"Making a Solver","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Finally populate the solver with problem data and solve:","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"let mut solver = DefaultSolver::new(&P, &q, &A, &b, &cones, settings);\n\nsolver.solve();","category":"page"},{"location":"rust/getting_started_rs/#Results","page":"Getting Started","title":"Results","text":"","category":"section"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Once the solver algorithm terminates you can inspect the solution using the solution field of the solver. ","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"println!(\"Solution status = {:?}\", solver.solution.status);\nprintln!(\"Primal solution = {:?}\", solver.solution.x);\nprintln!(\"Dual solution = {:?}\", solver.solution.z);\nprintln!(\"Primal slacks = {:?}\", solver.solution.s);","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"The outcome of the solve is specified in solver.solution.status and will be one of the following :","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"Status Code Description\nUnsolved Default value, only occurs prior to calling solve\nSolved Solution found\nPrimalInfeasible Problem is primal infeasible\nDualInfeasible Problem is dual infeasible\nAlmostSolved Solution found (reduced accuracy)\nAlmostPrimalInfeasible Problem is primal infeasible (reduced accuracy)\nAlmostDualInfeasible Problem is dual infeasible (reduced accuracy)\nMaxIterations Solver halted after reaching iteration limit\nMaxTime Solver halted after reaching time limit\nNumericalError Solver terminated with a numerical error\nInsufficientProgress Solver terminated due to lack of progress","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"The total solution time is available in solver.solution.solve_time. ","category":"page"},{"location":"rust/getting_started_rs/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_solution_warn.md\",\n plaintext = true)","category":"page"},{"location":"julia/getting_started_jl/#Getting-Started","page":"Getting Started","title":"Getting Started","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"This section describes the process of creating a Clarabel.jl model, populating its settings and problem data, solving the problem and obtaining and understanding results. The description here relates to Clarabel's native API. ","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"The first step is to bring the Clarabel solver and other required packages into scope in your code using:","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using Clarabel, SparseArrays, LinearAlgebra","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"The SparseArrays package from the Julia standard distribution defines the SparseMatrixCSC type for defining matrices in compressed sparse column format. ","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"JuMP / Convex.jl support: We provide an interface to MathOptInterface (MOI), which allows you to describe your problem in JuMP and Convex.jl. If you want to use JuMP or Convex.jl to model your problem instead, see the JuMP Interface and Convex.jl Interface sections.","category":"page"},{"location":"julia/getting_started_jl/#Problem-Format","page":"Getting Started","title":"Problem Format","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_problem.md\",\n plaintext = true)","category":"page"},{"location":"julia/getting_started_jl/#Objective-Function","page":"Getting Started","title":"Objective Function","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_objective.md\",\n plaintext = true)","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"The Clarabel default implementation in Julia expects matrix data in sparse SparseMatrixCSC format. We can define our cost data as","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"P = sparse([3. 1 -1; 0 4 2; 0 0 5])\nq = [1,2,-3.]","category":"page"},{"location":"julia/getting_started_jl/#Constraints","page":"Getting Started","title":"Constraints","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_constraints.md\",\n plaintext = true)","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"We can then define our constraint data as","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using SparseArrays\n\n# equality constraint\nAeq = [1. 1. -1.]\nbeq = [1.]\n\n# inequality constraint\nAineq = [0. 1. 0.;\n 0. 0. 1.]\nbineq = [2.,2.]\n\n# SOC constraint\nAsoc = -I(3)*1.\nbsoc = [0.,0.,0.]\n\n# Clarabel.jl constraint data\nA = sparse([Aeq; Aineq; Asoc])\nb = [beq;bineq;bsoc]","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Clarabel.jl expects to receive a vector of cone specifications. For the above constraints we should also define","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"# Clarabel.jl cone specification\ncones = [Clarabel.ZeroConeT(1), Clarabel.NonnegativeConeT(2), Clarabel.SecondOrderConeT(3)]","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"There is no restriction on the ordering of the cones that appear in cones, nor on the number of instances of each type that appear. The cones should be of type Vector{Clarabel.SupportedCone}, and your input vector b should be compatible with the sum of the cone dimensions.","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_constraints_note.md\",\n plaintext = true)","category":"page"},{"location":"julia/getting_started_jl/#Solver-Settings","page":"Getting Started","title":"Solver Settings","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Solver settings are stored in a Settings object and can be modified by the user. To create a Settings object just call the constructor:","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"settings = Clarabel.Settings()","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"To adjust those values, you can pass options and parameters as a key-value pair to the constructor or edit the corresponding field afterwards. For example, if you want to disable verbose printing and set a 5 second time limit on the solver, you can use","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"settings = Clarabel.Settings(verbose = false, time_limit = 5)\n\n# the following is equivalent\nsettings = Clarabel.Settings()\nsettings.verbose = false\nsettings.time_limit = 5","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"The full set of user configurable solver settings are listed in the API Reference.","category":"page"},{"location":"julia/getting_started_jl/#Making-a-Solver","page":"Getting Started","title":"Making a Solver","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"The problem data, user settings and workspace variables are all stored in a top level Solver type. First define an empty Solver:","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"solver = Clarabel.Solver()","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Then provide the solver with problem data using","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Clarabel.setup!(solver, P, q, A, b, cones, settings)","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"This takes an internal copy of all data parameters and initializes internal variables and other objects in the solver. The final settings argument is optional.","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Now you can solve your problem using:","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"solution = Clarabel.solve!(solver)\nsolution.x # primal solution\nsolution.z # dual solution\nsolution.s # slacks","category":"page"},{"location":"julia/getting_started_jl/#Results","page":"Getting Started","title":"Results","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Once the solver algorithm terminates you can inspect the solution using the solution object. The outcome of the solve is specified in solution.status and will be one of the following :","category":"page"},{"location":"julia/getting_started_jl/#Status-Codes","page":"Getting Started","title":"Status Codes","text":"","category":"section"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"Status Code Description\nSOLVED Solver terminated with a solution.\nPRIMAL_INFEASIBLE Problem is primal infeasible. Solution returned is a certificate of primal infeasibility.\nDUAL_INFEASIBLE Problem is dual infeasible. Solution returned is a certificate of dual infeasibility.\nALMOST_SOLVED Solver terminated with a solution (reduced accuracy).\nALMOST_PRIMAL_INFEASIBLE Problem is primal infeasible. Solution returned is a certificate of primal infeasibility (reduced accuracy).\nALMOST_DUAL_INFEASIBLE Problem is dual infeasible. Solution returned is a certificate of dual infeasibility (reduced accuracy).\nMAX_ITERATIONS Iteration limit reached before solution or infeasibility certificate found.\nMAX_TIME Time limit reached before solution or infeasibility certificate found.\nNUMERICAL_ERROR Solver terminated with a numerical error.\nINSUFFICIENT_PROGRESS Solver terminated due to lack of progress.","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"The total solution time (include combined setup! and solve! times) is given in solution.solve_time. Detailed information about the solve time and memory allocation can be found in the solver's timer field.","category":"page"},{"location":"julia/getting_started_jl/","page":"Getting Started","title":"Getting Started","text":"using Documenter\nDocumenter.md_include(\n source = \"docs/src/_common/getting_started_solution_warn.md\",\n plaintext = true)","category":"page"},{"location":"julia/jump/#JuMP-Interface","page":"JuMP Interface","title":"JuMP Interface","text":"","category":"section"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"Clarabel.jl implements support for MathOptInterface, and is therefore compatible with JuMP. This allows you to describe and modify your optimisation problem with JuMP and use Clarabel.jl as the backend solver.","category":"page"},{"location":"julia/jump/#Setting-Clarabel.jl-Backend","page":"JuMP Interface","title":"Setting Clarabel.jl Backend","text":"","category":"section"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"To specify Clarabel.jl as the solver for your JuMP model, load the solver module with using Clarabel and then configure Clarabel as the solver backend when initialising the JuMP model:","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"model = JuMP.Model(Clarabel.Optimizer)","category":"page"},{"location":"julia/jump/#Solver-Settings","page":"JuMP Interface","title":"Solver Settings","text":"","category":"section"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"Solver-specific settings can be passed after the Clarabel.Optimizer object. For example, if you want to adjust the maximum number of iterations and turn off verbose printing use","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"set_optimizer_attribute(model, \"verbose\", true)\nset_optimizer_attribute(model, \"max_iter\", 25)","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"The full list of available settings can be found in the Settings section of the API Reference.","category":"page"},{"location":"julia/jump/#Results","page":"JuMP Interface","title":"Results","text":"","category":"section"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"After solving the problem the result can be obtained using the standard JuMP commands. To see if the optimisation was successful use","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"JuMP.termination_status(model)\nJuMP.primal_status(model)","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"If a solution is available, the optimal objective value can be retrieved using","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"JuMP.objective_value(model)","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"and the value of a decision variable x can be obtained with","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"JuMP.value.(x)","category":"page"},{"location":"julia/jump/","page":"JuMP Interface","title":"JuMP Interface","text":"For more information on JuMP, see the JuMP documentation.","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"EditURL = \"../../../../examples/jl/example_qp.jl\"","category":"page"},{"location":"examples/jl/example_qp/#Quadratic-Program-(QP)-Example-in-Julia","page":"Julia","title":"Quadratic Program (QP) Example in Julia","text":"","category":"section"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"We will show how to solve the Basic QP example problem both natively in Clarabel.jl and also by solving with Clarabel.jl within either JuMP or Convex.jl.","category":"page"},{"location":"examples/jl/example_qp/#Clarabel.jl-native-interface","page":"Julia","title":"Clarabel.jl native interface","text":"","category":"section"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"using Clarabel, SparseArrays\n\nP = sparse([3. 0.;0. 2.].*2)\n\nq = [-1., -4.]\n\nA = sparse([1. -2.; #<-- LHS of equality constraint\n 1. 0.; #<-- LHS of inequality constraint (upper bound)\n 0. 1.; #<-- LHS of inequality constraint (upper bound)\n -1. 0.; #<-- LHS of inequality constraint (lower bound)\n 0. -1.; #<-- LHS of inequality constraint (lower bound)\n ])\n\nb = [0.; #<-- RHS of equality constraint\n ones(4)] #<-- RHS of inequality constraints\n\ncones =\n [Clarabel.ZeroConeT(1), #<--- for the equality constraint\n Clarabel.NonnegativeConeT(4)] #<--- for the inequality constraints\n\nsettings = Clarabel.Settings()\n\nsolver = Clarabel.Solver()\n\nClarabel.setup!(solver, P, q, A, b, cones, settings)\n\nresult = Clarabel.solve!(solver)\n\nnothing #hide","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"result #hide","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"result.x","category":"page"},{"location":"examples/jl/example_qp/#Using-JuMP","page":"Julia","title":"Using JuMP","text":"","category":"section"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"We can solve the same problem a little more easily by using Clarabel.jl as the backend solver within JuMP. Here is the same problem again:","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"using Clarabel, JuMP\n\nmodel = JuMP.Model(Clarabel.Optimizer)\nset_optimizer_attribute(model, \"verbose\", true)\n\n@variable(model, x[1:2])\n@constraint(model, x[1] == 2x[2])\n@constraint(model, -1 .<= x .<= 1)\n@objective(model, Min, 3x[1]^2 + 2x[2]^2 - x[1] - 4x[2])\n\noptimize!(model)","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"Here is the solution","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"JuMP.value.(x)","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"and the solver termination status again","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"JuMP.termination_status(model)","category":"page"},{"location":"examples/jl/example_qp/#Using-Convex.jl","page":"Julia","title":"Using Convex.jl","text":"","category":"section"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"We can likewise solve the same problem a using Clarabel.jl as the backend solver within Convex.jl. Here is the same problem one more time:","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"using Clarabel, Convex\n\nx = Variable(2)\nproblem = minimize(3square(x[1]) + 2square(x[2]) - x[1] - 4x[2])\nproblem.constraints = [x[1] == 2x[2]]\nproblem.constraints += [x >= -1; x <= 1]\nsolve!(problem, Clarabel.Optimizer; silent_solver = false)","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"Here is our solution","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"evaluate(x)","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"and the solver termination status again","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"problem.status","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"warning: Warning\nNote that in the Clarabel.jl output that follows the call to solve! using Convex.jl, the problem posed to the solver has been converted to a second-order cone program with a linear objective. You can see this because now nnz(P) == 0 (there is no quadratic term in the objective) and the solver reports two second order cone constraints.Although the solution will be the same, the required number of iterations and solve time are slightly higher. When solving problems with quadratic objectives in Clarabel.jl, it is generally preferable to use either the native Clarabel.jl interface or JuMP, both of which handle quadratic terms in the objective directly.","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"","category":"page"},{"location":"examples/jl/example_qp/","page":"Julia","title":"Julia","text":"This page was generated using Literate.jl.","category":"page"},{"location":"_common/getting_started_problem/","page":"-","title":"-","text":"Clarabel solves optimisation problems in the format:","category":"page"},{"location":"_common/getting_started_problem/","page":"-","title":"-","text":"beginarrayll textminimize textstylefrac12x^top Px + q^top x textsubject to Ax + s = b s in mathcalK endarray","category":"page"},{"location":"_common/getting_started_problem/","page":"-","title":"-","text":"with decision variables x in mathbbR^n, s in mathbbR^m and data matrices P=P^top succeq 0, q in mathbbR^n, A in mathbbR^m times n, and b in mathbbR^m. The convex cone mathcalK is a composition of smaller convex cones mathcalK = mathcalK_1 times mathcalK_2 dots mathcalK_p. Equality conditions can be modelled in this format using the solver's ZeroCone type. ","category":"page"},{"location":"_common/getting_started_problem/","page":"-","title":"-","text":"To initialize the solver with an optimisation problem we require three things:","category":"page"},{"location":"_common/getting_started_problem/","page":"-","title":"-","text":"The objective function, i.e. the matrix P and the vector q in frac12x^top P x + q^top x.\nThe data matrix A and vector b, along with a description of the composite cone mathcalK and the dimensions of its constituent pieces.\nA settings object that specifies how Clarabel solves the problem.","category":"page"},{"location":"_common/getting_started_objective/","page":"-","title":"-","text":"To set the objective function of your optimisation problem simply define the square positive semidefinite matrix P in mathrmR^ntimes n and the vector q in mathrmR^n.","category":"page"},{"location":"_common/getting_started_objective/","page":"-","title":"-","text":"Suppose that we have a problem with decision variable x in mathbbR^3 and our objective function is:","category":"page"},{"location":"_common/getting_started_objective/","page":"-","title":"-","text":"beginequation*\nmin \nfrac12\nleft\nbeginarrayl\nx_1 x_2 x_3\nendarray\nright\n^T\nleft\nbeginarrayrrr\n30 10 -10 \n10 40 20 \n -10 20 50\nendarray\nright\nleft\nbeginarrayl\nx_1 x_2 x_3\nendarray\nright\n+\nleft\nbeginarrayr\n1 2 -3\nendarray\nright^T\nleft\nbeginarrayl\nx_1 x_2 x_3\nendarray\nright\nendequation*","category":"page"},{"location":"_common/getting_started_objective/","page":"-","title":"-","text":"Clarabel expects the P matrix to be supplied in Compressed Sparse Column format. P is assumed by the solver to be symmetric and only values in the upper triangular part of P are needed by the solver, i.e. you only need to provide","category":"page"},{"location":"_common/getting_started_objective/","page":"-","title":"-","text":"beginequation*\nP =\nleft\nbeginarrayrrr\n30 10 -10 \n 40 20 \n 50\nendarray\nright\nendequation*","category":"page"},{"location":"rust/installation_rs/#Installation","page":"Installation","title":"Installation","text":"","category":"section"},{"location":"rust/installation_rs/#Using-Cargo","page":"Installation","title":"Using Cargo","text":"","category":"section"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"Clarabel.rs is available through the Rust registry at crates.io and can be imported directly as a dependency in your project. Just add","category":"page"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"[dependencies]\nclarabel = \"0\" ","category":"page"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"in your project's Cargo.toml file to obtain the latest version.","category":"page"},{"location":"rust/installation_rs/#Direct-from-source","page":"Installation","title":"Direct from source","text":"","category":"section"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"You can also download and build the repository directly from Github: ","category":"page"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"git clone https://github.com/oxfordcontrol/Clarabel.rs\ncd Clarabel.rs\ncargo build --release","category":"page"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"To check that your installation worked, you can run","category":"page"},{"location":"rust/installation_rs/","page":"Installation","title":"Installation","text":"cargo run --example qp","category":"page"},{"location":"","page":"Home","title":"Home","text":"Clarabel is an interior point numerical solver for convex optimization problems using a novel homogeneous embedding. The Clarabel package solves the following problem:","category":"page"},{"location":"","page":"Home","title":"Home","text":"beginarrayr\ntextminimize frac12x^T P x + q^T x2ex\n textsubject to Ax + s = b 1ex\n s in mathcalK\n endarray","category":"page"},{"location":"","page":"Home","title":"Home","text":"with decision variables x in mathbbR^n, s in mathbbR^m and data matrices P=P^top succeq 0, q in mathbbR^n, A in mathbbR^m times n, and b in mathbbR^m. The convex set mathcalK is a composition of convex cones.","category":"page"},{"location":"","page":"Home","title":"Home","text":"Clarabel is available in either a native Julia or a native Rust implementation. Additional language interfaces (Python, C/C++ and R) are available for the Rust version.","category":"page"},{"location":"#Features","page":"Home","title":"Features","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Versatile: Clarabel solves linear programs (LPs), quadratic programs (QPs), second-order cone programs (SOCPs) and semidefinite programs (SDPs). It also solves problems with exponential, power cone and generalized power cone constraints.\nQuadratic objectives: Unlike interior point solvers based on the standard homogeneous self-dual embedding (HSDE) model, Clarabel handles quadratic objective without requiring any epigraphical reformulation of its objective function. It can therefore be significantly faster than other HSDE-based solvers for problems with quadratic objective functions.\nInfeasibility detection: Infeasible problems are detected using using a homogeneous embedding technique.\nArbitrary precision types: You can solve problems with any floating point precision, e.g. Float32 or Julia's BigFloat type in Julia and f32 or f64 types in Rust.\nOpen Source: Our code is available on GitHub and distributed under the Apache 2.0 License. The Julia implementation is here. The Rust implementation and Python interface is here.","category":"page"},{"location":"#Credits","page":"Home","title":"Credits","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"The following people are involved in the development of Clarabel:","category":"page"},{"location":"","page":"Home","title":"Home","text":"Paul Goulart (main development, maths and algorithms)\nYuwen Chen (maths and algorithms)","category":"page"},{"location":"","page":"Home","title":"Home","text":"All contributors are affiliated with the Control Group of the Department of Engineering Science at the University of Oxford.","category":"page"},{"location":"","page":"Home","title":"Home","text":"If this project is useful for your work please consider","category":"page"},{"location":"","page":"Home","title":"Home","text":"Citing the relevant papers\nLeaving a star on the GitHub repository (Julia) : (Rust).","category":"page"},{"location":"#License","page":"Home","title":"License","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Clarabel.jl and Clarabel.rs are licensed under the Apache License 2.0 (Julia) : (Rust).","category":"page"},{"location":"examples/rs/example_socp/","page":"Rust","title":"Rust","text":"Complete Cargo projects for all Rust examples can be found in examples/rs.","category":"page"},{"location":"examples/rs/example_socp/","page":"Rust","title":"Rust","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/rs/example_socp/src/main.rs\",\n language = :rust)","category":"page"},{"location":"examples/jl/README/","page":"-","title":"-","text":"Julia examples in this directory are automatically built from the /examples/jl using the Literate.jl package during documentation build. ","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"If you find Clarabel useful in your work, please consider citing one or more of the following papers. For the solver itself:","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"@misc{Clarabel_2024,\n title={Clarabel: An interior-point solver for conic programs with quadratic objectives}, \n author={Paul J. Goulart and Yuwen Chen},\n year={2024},\n eprint={2405.12762},\n archivePrefix={arXiv},\n primaryClass={math.OC}\n}","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"A preprint is available here.","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"If you use Clarabel to solve SDPs with decomposable structure:","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"@InProceedings{Garstka_2020,\n author = {Michael Garstka and Mark Cannon and Paul Goulart},\n title = {A clique graph based merging strategy for decomposable {SDPs}},\n year = {2020},\n note = {21th IFAC World Congress},\n number = {2},\n pages = {7355-7361},\n volume = {53},\n doi = {10.1016/j.ifacol.2020.12.1255},\n issn = {2405-8963},\n journal = {IFAC-PapersOnLine},\n}","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"A preprint is available here.","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"If you use Clarabel to solve problems with generalized power cones:","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"@misc{chen2023efficient,\n title={An Efficient IPM Implementation for A Class of Nonsymmetric Cones}, \n author={Yuwen Chen and Paul Goulart},\n year={2023},\n eprint={2305.12275},\n archivePrefix={arXiv},\n primaryClass={math.OC}\n}","category":"page"},{"location":"citing/","page":"Citing Clarabel","title":"Citing Clarabel","text":"A preprint is available here.","category":"page"},{"location":"contributing/#Contributing","page":"Contributing","title":"Contributing","text":"","category":"section"},{"location":"contributing/","page":"Contributing","title":"Contributing","text":"Contributions are always welcome:","category":"page"},{"location":"contributing/","page":"Contributing","title":"Contributing","text":"Please report any issues and bugs that you encounter in Issues.\nAs an open source project we are also interested in any projects and applications that use Clarabel. Please let us know via email to: paul.goulart@eng.ox.ac.uk.","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"EditURL = \"../../../../examples/jl/example_socp.jl\"","category":"page"},{"location":"examples/jl/example_socp/#SOCP-Example-in-Julia","page":"Julia","title":"SOCP Example in Julia","text":"","category":"section"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"We will show how to solve this problem both natively in Clarabel.jl and also by solving with Clarabel.jl within JuMP.","category":"page"},{"location":"examples/jl/example_socp/#Clarabel.jl-native-interface","page":"Julia","title":"Clarabel.jl native interface","text":"","category":"section"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"using Clarabel, SparseArrays\n\nP = sparse([0. 0.;0. 1.].*2)\n\nq = [0., 0.]\n\nA = sparse([0. 0.\n -2. 0.;\n 0. -1.])\nb = [ 1.\n -2.;\n -2.]\n\ncones = [Clarabel.SecondOrderConeT(3)]\n\nsettings = Clarabel.Settings(max_iter = 15, verbose = true)\n\nsolver = Clarabel.Solver()\n\nClarabel.setup!(solver, P, q, A, b, cones, settings)\n\nresult = Clarabel.solve!(solver)\n\nnothing #hide","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"result #hide","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"result.x","category":"page"},{"location":"examples/jl/example_socp/#Using-JuMP","page":"Julia","title":"Using JuMP","text":"","category":"section"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"We can solve the same problem using Clarabel.jl as the backend solver within JuMP. Here is the same problem again:","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"using Clarabel, JuMP\n\nmodel = JuMP.Model(Clarabel.Optimizer)\nset_optimizer_attribute(model, \"verbose\", true)\n\n@variable(model, x[1:2])\n@constraint(model, [1, 2x[1]-2, x[2] - 2] in SecondOrderCone())\n@objective(model, Min, x[2]^2 )\n\noptimize!(model)","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"Here is the solution","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"JuMP.value.(x)","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"and the solver termination status again","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"JuMP.termination_status(model)","category":"page"},{"location":"examples/jl/example_socp/#Using-Convex.jl","page":"Julia","title":"Using Convex.jl","text":"","category":"section"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"One more time using Clarabel.jl as the backend solver within Convex.jl:","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"using Clarabel, Convex\n\nx = Variable(2)\nproblem = minimize(square(x[2]))\nproblem.constraints = [norm([2x[1];x[2]] - [2;2], 2) <= 1]\nsolve!(problem, Clarabel.Optimizer; silent_solver = false)","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"Here is our solution","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"evaluate(x)","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"and the solver termination status again","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"problem.status","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"","category":"page"},{"location":"examples/jl/example_socp/","page":"Julia","title":"Julia","text":"This page was generated using Literate.jl.","category":"page"},{"location":"examples/rs/example_powcone/","page":"Rust","title":"Rust","text":"Complete Cargo projects for all Rust examples can be found in examples/rs.","category":"page"},{"location":"examples/rs/example_powcone/","page":"Rust","title":"Rust","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/rs/example_powcone/src/main.rs\",\n language = :rust)","category":"page"},{"location":"api_jl/#Julia-API-Reference","page":"Julia API","title":"Julia API Reference","text":"","category":"section"},{"location":"api_jl/#api-solver","page":"Julia API","title":"Solver and main API","text":"","category":"section"},{"location":"api_jl/","page":"Julia API","title":"Julia API","text":"Clarabel.Solver\nClarabel.setup!\nClarabel.solve!","category":"page"},{"location":"api_jl/#Clarabel.Solver","page":"Julia API","title":"Clarabel.Solver","text":"Solver{T <: AbstractFloat}()\n\nInitializes an empty Clarabel solver that can be filled with problem data using:\n\nsetup!(solver, P, q, A, b, cones, [settings]).\n\n\n\n\n\n","category":"type"},{"location":"api_jl/#Clarabel.setup!","page":"Julia API","title":"Clarabel.setup!","text":"setup!(solver, P, q, A, b, cones, [settings])\n\nPopulates a Solver with a cost function defined by P and q, and one or more conic constraints defined by A, b and a description of a conic constraint composed of cones whose types and dimensions are specified by cones.\n\nThe solver will be configured to solve the following optimization problem:\n\nmin 1/2 x'Px + q'x\ns.t. Ax + s = b, s ∈ K\n\nAll data matrices must be sparse. The matrix P is assumed to be symmetric and positive semidefinite, and only the upper triangular part is used.\n\nThe cone K is a composite cone. To define the cone the user should provide a vector of cone specifications along with the appropriate dimensional information. For example, to generate a cone in the nonnegative orthant followed by a second order cone, use:\n\ncones = [Clarabel.NonnegativeConeT(dim_1),\n Clarabel.SecondOrderConeT(dim_2)]\n\nIf the argument 'cones' is constructed incrementally, the should should initialize it as an empty array of the supertype for all allowable cones, e.g.\n\ncones = Clarabel.SupportedCone[]\npush!(cones,Clarabel.NonnegativeConeT(dim_1))\n...\n\nThe optional argument settings can be used to pass custom solver settings:\n\nsettings = Clarabel.Settings(verbose = true)\nsetup!(model, P, q, A, b, cones, settings)\n\nTo solve the problem, you must make a subsequent call to solve!\n\n\n\n\n\n","category":"function"},{"location":"api_jl/#Clarabel.solve!","page":"Julia API","title":"Clarabel.solve!","text":"solve!(solver)\n\nComputes the solution to the problem in a Clarabel.Solver previously defined in setup!.\n\n\n\n\n\n","category":"function"},{"location":"api_jl/#api-cones","page":"Julia API","title":"SupportedCone","text":"","category":"section"},{"location":"api_jl/","page":"Julia API","title":"Julia API","text":"Clarabel.SupportedCone","category":"page"},{"location":"api_jl/#Clarabel.SupportedCone","page":"Julia API","title":"Clarabel.SupportedCone","text":"SupportedCone\n\nAn abstract type use by the Clarabel API used when passing cone specifications to the solver setup!. The currently supported concrete types are:\n\nZeroConeT : The zero cone. Used to define equalities.\nNonnegativeConeT: The nonnegative orthant.\nSecondOrderConeT: The second order / Lorentz / ice-cream cone.\nExponentialConeT: The exponential cone (in R^3)\nPowerConeT : The power cone with power α (in R^3)\nGenPowerConeT : The generalized power cone \nPSDTriangleConeT: The positive semidefinite cone (triangular format).\n\n\n\n\n\n","category":"type"},{"location":"api_jl/#api-solverstatus","page":"Julia API","title":"Solver Status","text":"","category":"section"},{"location":"api_jl/","page":"Julia API","title":"Julia API","text":"Clarabel.SolverStatus","category":"page"},{"location":"api_jl/#Clarabel.SolverStatus","page":"Julia API","title":"Clarabel.SolverStatus","text":"SolverStatus\n\nAn Enum of of possible conditions set by solve!.\n\nIf no call has been made to solve!, then the SolverStatus is:\n\nUNSOLVED: The algorithm has not started.\n\nOtherwise:\n\nSOLVED : Solver terminated with a solution.\nPRIMAL_INFEASIBLE : Problem is primal infeasible. Solution returned is a certificate of primal infeasibility.\nDUAL_INFEASIBLE : Problem is dual infeasible. Solution returned is a certificate of dual infeasibility.\nALMOST_SOLVED : Solver terminated with a solution (reduced accuracy).\nALMOST_PRIMAL_INFEASIBLE : Problem is primal infeasible. Solution returned is a certificate of primal infeasibility (reduced accuracy).\nALMOST_DUAL_INFEASIBLE : Problem is dual infeasible. Solution returned is a certificate of dual infeasibility (reduced accuracy).\nMAX_ITERATIONS : Iteration limit reached before solution or infeasibility certificate found.\nMAX_TIME : Time limit reached before solution or infeasibility certificate found.\nNUMERICAL_ERROR : Solver terminated with a numerical error.\nINSUFFICIENT_PROGRESS : Solver terminated due to lack of progress.\n\n\n\n\n\n","category":"type"},{"location":"examples/py/example_socp/","page":"Python","title":"Python","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_socp.py\",\n language = :python)","category":"page"},{"location":"examples/rs/example_qp/","page":"Rust","title":"Rust","text":"Complete Cargo projects for all Rust examples can be found in examples/rs.","category":"page"},{"location":"examples/rs/example_qp/","page":"Rust","title":"Rust","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/rs/example_qp/src/main.rs\",\n language = :rust)","category":"page"},{"location":"user_guide_r/#user-guide-r","page":"R","title":"R Installation and User Guide","text":"","category":"section"},{"location":"user_guide_r/","page":"R","title":"R","text":"The R interface to Clarabel can be installed either directly or via CRAN.","category":"page"},{"location":"user_guide_r/","page":"R","title":"R","text":"The installation and user guide can be found here.","category":"page"},{"location":"_common/getting_started_solution_warn/","page":"-","title":"-","text":"warning: Warning\nBe careful to retrieve solver solutions from the solution that is returned by the solver, or directly from a solver object from the solver.solution field. Do not use the solver.variables, since these have both homogenization and equilibration scaling applied and therefore do not solve the optimization problem posed to the solver.","category":"page"},{"location":"examples/example_qp/#QP-Example","page":"Problem Description","title":"QP Example","text":"","category":"section"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"Suppose that we want to solve the following 2-dimensional quadratic programming problem:","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"beginarrayll textminimize 3x_1^2 + 2x_2^2 - x_1 - 4x_2\ntextsubject to -1 leq x leq 1 x_1 = 2x_2\nendarray","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"We will show how to solve this problem through each of Clarabel's supported languages and interfaces.","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"In each case the first step is to put the problem data into the standard form expected by the solver.","category":"page"},{"location":"examples/example_qp/#Objective-function","page":"Problem Description","title":"Objective function","text":"","category":"section"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"The Clarabel solver's default configuration expects problem data in the form frac12x^top P x + q^top x. We therefore define the objective function data as","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"P = 2 cdot beginbmatrix 3 0 0 2endbmatrix\ntextrmand\nq = beginbmatrix -1 -4endbmatrix","category":"page"},{"location":"examples/example_qp/#Constraints","page":"Problem Description","title":"Constraints","text":"","category":"section"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"The solver's default configuration expects constraints in the form Ax + s = b, where s in mathcalK for some composite cone mathcalK. We have 1 equality constraint and 4 inequalities, so we require the first element of s to be zero (i.e. the first constraint will correspond to the equality) and all other elements s_i ge 0. Our cone constraint on s is therefore","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"s in mathcal K = 0^1 times mathbbR^4_ge 0","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"Define the constraint data as","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"A =\nfootnotesizebeginbmatrix*r 1 -2 1 0 0 1 -1 0 0 -1endbmatrix*\ntextrmand\n b=\nfootnotesizebeginbmatrix 0 1 1 1 1 endbmatrix","category":"page"},{"location":"examples/example_qp/","page":"Problem Description","title":"Problem Description","text":"Note that Clarabel expects inputs in Compressed Sparse Column (CSC) format for both P and A.","category":"page"},{"location":"user_guide_chordal/#user-guide-chordal","page":"Chordal Decomposition","title":"Chordal Decomposition","text":"","category":"section"},{"location":"user_guide_chordal/","page":"Chordal Decomposition","title":"Chordal Decomposition","text":"Clarabel implements a chordal decomposition and clique merging method to solve large-scale semidefinite programming problems. If the problem has favorable structure, this method can decompose a sparse positive semidefiniteness constraint on a large semidefinite cone into a collection of semidefinite constraints on a collection of smaller cones. This can lead to significant computational savings in terms of both memory and time. ","category":"page"},{"location":"user_guide_chordal/","page":"Chordal Decomposition","title":"Chordal Decomposition","text":"Clarabel uses the same decomposition strategy as COSMO.jl. For details see our paper on clique merging techniques and this presentation by Michael Garstka.","category":"page"},{"location":"julia/installation_jl/#Installation","page":"Installation","title":"Installation","text":"","category":"section"},{"location":"julia/installation_jl/","page":"Installation","title":"Installation","text":"Clarabel.jl can be installed using the Julia package manager for Julia v1.0 and higher. Inside the Julia REPL, type ] to enter the Pkg REPL mode then run","category":"page"},{"location":"julia/installation_jl/","page":"Installation","title":"Installation","text":"pkg> add Clarabel","category":"page"},{"location":"julia/installation_jl/","page":"Installation","title":"Installation","text":"If you want to install the latest version from the github repository run","category":"page"},{"location":"julia/installation_jl/","page":"Installation","title":"Installation","text":"pkg> add Clarabel#main","category":"page"},{"location":"python/installation_py/#Installation","page":"Installation","title":"Installation","text":"","category":"section"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"The Clarabel Python interface supports version 3.7 or newer. To install directly, use:","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"pip install clarabel","category":"page"},{"location":"python/installation_py/#Installing-from-source","page":"Installation","title":"Installing from source","text":"","category":"section"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"You can also download and build the repository directly from Github. You will need to have a working Rust installation to compile the Python interface.","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"To obtain the source: ","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"git clone https://github.com/oxfordcontrol/Clarabel.rs\ncd Clarabel.rs","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"The Python interface to the Rust solver is implemented using PyO3 and can be built with Maturin. First create and activate a python virtual environment for your build:","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"python3 -m venv .env\nsource .env/bin/activate","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"Install maturin in your virtual environment:","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"pip install maturin","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"Then compile the Rust source with PyO3 bindings enabled:","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"maturin develop --release ","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"To check that Clarabel works within the virtual environment, you can then run","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"python examples/python/example_qp.py","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"To compile and install the solver outside of the virtual environment, at the last step you can instead run","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"maturin build -i python --release --features python","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"inside the virtual environment to produce a .whl. Then outside the virtual environment run","category":"page"},{"location":"python/installation_py/","page":"Installation","title":"Installation","text":"python3 -m pip install <.whl-file-you-just-built>","category":"page"},{"location":"_common/getting_started_constraints/","page":"-","title":"-","text":"The Clarabel interface expects constraints to be presented in the single vectorized form Ax + s = b s in mathcalK, where mathcalK = mathcalK_1 times dots times mathcalK_p and each mathcalK_i is one of the solver's supported cone types.","category":"page"},{"location":"_common/getting_started_constraints/","page":"-","title":"-","text":"Suppose that we have a problem with decision variable x in mathbbR^3 and our constraints are:","category":"page"},{"location":"_common/getting_started_constraints/","page":"-","title":"-","text":"A single equality constraint x_1 + x_2 - x_3 = 1. \nA pair of inequalities such that x_2 and x_3 are each less than 2.\nA second order cone constraint on the 3-dimensional vector x. ","category":"page"},{"location":"_common/getting_started_constraints/","page":"-","title":"-","text":"For the three constraints above, we have","category":"page"},{"location":"_common/getting_started_constraints/","page":"-","title":"-","text":"\nbeginalign*\n\nA_eq =\nleft\nbeginarraylll\n1 1 -1\nendarray\nright\nquad \nb_eq =\nleft\nbeginarrayl\n1\nendarray\nright\n\n4ex\n\nA_ineq =\nleft\nbeginarraylll\n0 1 0 \n0 0 1\nendarray\nright\nquad \nb_ineq =\nleft\nbeginarrayl\n22\nendarray\nright\n\n4ex\n\nA_soc =\nleft\nbeginarrayrrr\n-1 0 0 \n 0 -1 0 \n 0 0 -1\nendarray\nright\nquad \nb_soc =\nleft\nbeginarrayl\n0 0 0\nendarray\nright\n\nendalign*\n","category":"page"},{"location":"api_settings/#Clarabel-Solver-Settings","page":"Solver Settings","title":"Clarabel Solver Settings","text":"","category":"section"},{"location":"api_settings/","page":"Solver Settings","title":"Solver Settings","text":"The Clarabel solver supports a variety of configuration options. The Julia, Rust and Python and interfaces all support the same set of options with identical field names.","category":"page"},{"location":"api_settings/","page":"Solver Settings","title":"Solver Settings","text":"warning: Warning\nThe solver defaults are configured to give good general performance for most problems, but assume that the problem data is of 64 bit float type. Although the Rust and Julia solvers will accept 32 bit types instead (i.e. Float32 in Julia or f32 in Rust), the solver is unlikely to perform well unless the tolerances are relaxed. ","category":"page"},{"location":"api_settings/","page":"Solver Settings","title":"Solver Settings","text":"","category":"page"},{"location":"api_settings/","page":"Solver Settings","title":"Solver Settings","text":"The full set of options follows below.","category":"page"},{"location":"api_settings/#api-settings","page":"Solver Settings","title":"Settings","text":"","category":"section"},{"location":"api_settings/","page":"Solver Settings","title":"Solver Settings","text":"Clarabel.Settings","category":"page"},{"location":"api_settings/#Clarabel.Settings","page":"Solver Settings","title":"Clarabel.Settings","text":"Argument Default Value Description\n \nMain Algorithm Settings \n \nmax_iter 200 maximum number of iterations\ntime_limit Inf maximum run time (seconds)\nverbose true verbose printing\nmax_step_fraction 0.99 maximum interior point step length\n \nFull Accuracy Settings \ntol_gap_abs 1e-8 absolute duality gap tolerance\ntol_gap_rel 1e-8 relative duality gap tolerance\ntol_feas 1e-8 feasibility check tolerance (primal and dual)\ntol_infeas_abs 1e-8 absolute infeasibility tolerance (primal and dual)\ntol_infeas_rel 1e-8 relative infeasibility tolerance (primal and dual)\ntol_ktratio 1e-6 κ/τ tolerance\n \nReduced Accuracy Settings \nreduced_tol_gap_abs 5e-5 reduced absolute duality gap tolerance\nreduced_tol_gap_rel 5e-5 reduced relative duality gap tolerance\nreduced_tol_feas 1e-4 reduced feasibility check tolerance (primal and dual)\nreduced_tol_infeas_abs 5e-5 reduced absolute infeasibility tolerance (primal and dual)\nreduced_tol_infeas_rel 5e-5 reduced relative infeasibility tolerance (primal and dual)\nreduced_tol_ktratio 1e-4 reduced κ/τ tolerance\n \nData Equilibration Settings \nequilibrate_enable true enable data equilibration pre-scaling\nequilibrate_max_iter 10 maximum equilibration scaling iterations\nequilibrate_min_scaling 1e-4 minimum equilibration scaling allowed\nequilibrate_max_scaling 1e+4 maximum equilibration scaling allowed\n \nStep Size Settings \nlinesearch_backtrack_step 0.8 linesearch backtracking\nmin_switch_step_length 1e-1 minimum step size allowed for asymmetric cones with PrimalDual scaling\nmin_terminate_step_length 1e-4 minimum step size allowed for symmetric cones & asymmetric cones with Dual scaling\n \nLinear Solver Settings \ndirect_kkt_solver true use a direct linear solver method (required true)\ndirect_solve_method :qdldl direct linear solver (e.g. :qdldl, :mkl, :panua, :ma57, :cholmod, :faer)\nstatic_regularization_enable true enable KKT static regularization\nstatic_regularization_eps 1e-8 KKT static regularization parameter\nstatic_regularization_proportional eps(T)^2 additional regularization parameter w.r.t. the maximum abs diagonal term\ndynamic_regularization_enable true enable KKT dynamic regularization\ndynamic_regularization_eps 1e-13 KKT dynamic regularization threshold\ndynamic_regularization_delta 2e-7 KKT dynamic regularization shift\niterative_refinement_enable true KKT direct solve with iterative refinement\niterative_refinement_reltol 1e-12 iterative refinement relative tolerance\niterative_refinement_abstol 1e-12 iterative refinement absolute tolerance\niterative_refinement_max_iter 10 iterative refinement maximum iterations\niterative_refinement_stop_ratio 5.0 iterative refinement stalling tolerance\n \n\nPreprocessing Settings presolve_enable | true | enable presolve constraint reduction || __Chordal Decomposition Settings|| chordal_decomposition_enable | true | enable chordal decomposition chordal_decomposition_mergemethod | :cliquegraph | chordal decomposition merge method (:none, :parentchild or :cliquegraph) chordal_decomposition_compact | true | assemble decomposed system in \"compact\" form chordal_decomposition_complete_dual | false | complete PSD dual variables after decomposition\n\n\n\n\n\n","category":"type"},{"location":"examples/py/example_qp/","page":"Python","title":"Python","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_qp.py\",\n language = :python)","category":"page"},{"location":"examples/jl/example_powcone/","page":"Julia","title":"Julia","text":"EditURL = \"../../../../examples/jl/example_powcone.jl\"","category":"page"},{"location":"examples/jl/example_powcone/","page":"Julia","title":"Julia","text":"using Clarabel, SparseArrays\n\nP = spzeros(6,6)\n\nq = [0., 0., -1., 0., 0., -1.]\n\nA = sparse([\n -1. 0. 0. 0. 0. 0.;\n 0. -1. 0. 0. 0. 0.;\n 0. 0. -1. 0. 0. 0.;\n 0. 0. 0. -1. 0. 0.;\n 0. 0. 0. 0. -1. 0.;\n 0. 0. 0. 0. 0. -1.;\n 1. 2. 0. 3. 0. 0.;\n 0. 0. 0. 0. 1. 0.])\n\nb = [0., 0., 0., 0., 0., 0., 3., 1.]\n\ncones = [Clarabel.PowerConeT(0.6), Clarabel.PowerConeT(0.1), Clarabel.ZeroConeT(2)]\n\nsolver = Clarabel.Solver()\n\nsettings = Clarabel.Settings()\n\nClarabel.setup!(solver, P, q, A, b, cones, settings)\n\nresult = Clarabel.solve!(solver)\n\nnothing #hide","category":"page"},{"location":"examples/jl/example_powcone/","page":"Julia","title":"Julia","text":"result #hide","category":"page"},{"location":"examples/jl/example_powcone/","page":"Julia","title":"Julia","text":"result.x","category":"page"},{"location":"examples/jl/example_powcone/","page":"Julia","title":"Julia","text":"","category":"page"},{"location":"examples/jl/example_powcone/","page":"Julia","title":"Julia","text":"This page was generated using Literate.jl.","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"EditURL = \"../convex_jl.jl\"","category":"page"},{"location":"literate/build/convex_jl/#Convex.jl-Interface","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"","category":"section"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"Clarabel.jl implements support for MathOptInterface, and is therefore compatible with Convex.jl. This allows you to describe and modify your optimisation problem with Convex.jl and use Clarabel as the backend solver.","category":"page"},{"location":"literate/build/convex_jl/#Setting-Clarabel.jl-Backend","page":"Convex.jl Interface","title":"Setting Clarabel.jl Backend","text":"","category":"section"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"You should construct your problem in the usual way in Convex.jl, and then solve using Clarabel.Optimizer, i.e. by calling solve! with","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"solve!(problem, Clarabel.Optimizer)","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"where problem is an object of type Convex.Problem.","category":"page"},{"location":"literate/build/convex_jl/#Convex.jl-or-JuMP?","page":"Convex.jl Interface","title":"Convex.jl or JuMP?","text":"","category":"section"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"Clarabel.jl supports both Convex.jl and JuMP via MathOptInterface. Both packages are excellent and can make problem construction considerably easier than via the solver's native interface.","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"For problems with quadratic objective functions, JuMP is generally preferred when using Clarabel.jl since it will keep the quadratic function in the objective rather than reformulating the problem to a form with a linear cost and additional second-order cone constraints. Clarabel.jl natively supports quadratic objectives and solve times are generally faster if this reformulation is avoided.","category":"page"},{"location":"literate/build/convex_jl/#Arbitrary-Precision-Arithmetic","page":"Convex.jl Interface","title":"Arbitrary Precision Arithmetic","text":"","category":"section"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"Clarabel.jl supports arbitrary precision arithmetic for Convex.jl. Here is the QP Example implemented using BigFloat types.","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"#hide setprecision(BigFloat,256)\nusing Clarabel, Convex\n\nx = Variable(2)\nobjective = 3square(x[1]) + 2square(x[2]) - x[1] - 4x[2]\nproblem = minimize(objective; numeric_type = BigFloat)\nproblem.constraints = [x[1] == 2x[2]]\nproblem.constraints += [x >= -1; x <= 1]\nsolve!(problem, Clarabel.Optimizer{BigFloat}; silent_solver = false)","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"","category":"page"},{"location":"literate/build/convex_jl/","page":"Convex.jl Interface","title":"Convex.jl Interface","text":"This page was generated using Literate.jl.","category":"page"},{"location":"api_cone_types/#api-cone-types","page":"Supported Cone Types","title":"Supported Cone Types","text":"","category":"section"},{"location":"api_cone_types/","page":"Supported Cone Types","title":"Supported Cone Types","text":"Clarabel natively supports optimization problems with conic constraints defined on the following cones:","category":"page"},{"location":"api_cone_types/","page":"Supported Cone Types","title":"Supported Cone Types","text":"Cone Type Constructor Definition\nZero cone ZeroConeT(n) 0 ^n\nNonnegative Orthant NonnegativeConeT(n) x in mathbbR^n x_i ge 0 forall i=1dotsmathrmn \nSecond-Order Cone SecondOrderConeT(n) (tx) in mathbbR^n x_2 leq t \nExponential Cone ExponentialConeT() (x y z) y 0 ye^xy z \nPower Cone PowerConeT(a) (x y z) x^a y^(1-a) geq z (xy) geq 0 with a in (01)\nGeneralized Power Cone GenPowerConeT(a,n) (x y) in mathbbR^len(a) times mathbbR^n prodlimits_a_i in a x_i^a_i geq y_2 x ge 0 with a_i in (01) and sum a_i = 1\nPositive Semidefinite Cone (triangular part) PSDTriangleConeT(n) Upper triangular part of the positive semidefinite cone mathbbS^n_+. The elements x of this cone represent the columnwise stacking of the upper triangular part of a positive semidefinite matrix X in mathbbS^n_+, so that x in mathbbR^d with d = n(n+1)2","category":"page"},{"location":"examples/jl/example_expcone/","page":"Julia","title":"Julia","text":"EditURL = \"../../../../examples/jl/example_expcone.jl\"","category":"page"},{"location":"examples/jl/example_expcone/","page":"Julia","title":"Julia","text":"using Clarabel, SparseArrays\n\nP = spzeros(3,3)\n\nq = [-1.,0.,0.]\n\nA = sparse([\n -1. 0. 0.;\n 0. -1. 0.;\n 0. 0. -1.;\n 0. 1. 0.;\n 0. 0. 1.]);\n\nb = [0.,0.,0.,1.,exp(5.)];\n\ncones = [Clarabel.ExponentialConeT(), Clarabel.ZeroConeT(2)]\n\nsolver = Clarabel.Solver()\n\nsettings = Clarabel.Settings()\n\nClarabel.setup!(solver, P, q, A, b, cones, settings)\n\nresult = Clarabel.solve!(solver)\n\nnothing #hide","category":"page"},{"location":"examples/jl/example_expcone/","page":"Julia","title":"Julia","text":"result #hide","category":"page"},{"location":"examples/jl/example_expcone/","page":"Julia","title":"Julia","text":"result.x","category":"page"},{"location":"examples/jl/example_expcone/","page":"Julia","title":"Julia","text":"","category":"page"},{"location":"examples/jl/example_expcone/","page":"Julia","title":"Julia","text":"This page was generated using Literate.jl.","category":"page"},{"location":"examples/py/example_expcone/","page":"Python","title":"Python","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/py/example_expcone.py\",\n language = :python)","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"EditURL = \"../../../../examples/jl/example_sdp.jl\"","category":"page"},{"location":"examples/jl/example_sdp/#Semidefinite-Programming-(SDP)-in-Julia","page":"Julia","title":"Semidefinite Programming (SDP) in Julia","text":"","category":"section"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"We will show how to solve the Basic QP example problem both natively in Clarabel.jl and also by solving with Clarabel.jl within either JuMP or Convex.jl.","category":"page"},{"location":"examples/jl/example_sdp/#Clarabel.jl-native-interface","page":"Julia","title":"Clarabel.jl native interface","text":"","category":"section"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"using Clarabel, SparseArrays, LinearAlgebra\n\nn = 3\nnvec = Int(n*(n+1)/2)\n\nP = spzeros(nvec,nvec)\n\nq = [1.,0.,1.,0.,0.,1.]\n\nA1 = -Diagonal([ #<-- LHS of SDP constraint\n 1., sqrt(2), 1., sqrt(2), sqrt(2), 1.\n])\nA2 = [1. 2(2.) 3. 2(4.) 2(5.) 6.] #<-- LHS of equality constraint\nA = sparse([A1;A2]);\n\nb = [zeros(nvec); #<-- RHS of SDP constraint\n 1.] #<-- RHS of equality constraint\n\ncones =\n [Clarabel.PSDTriangleConeT(n), #<--- for the SDP constraint\n Clarabel.ZeroConeT(1)] #<--- for the equality constraints\n\nsettings = Clarabel.Settings()\n\nsolver = Clarabel.Solver()\n\nClarabel.setup!(solver, P, q, A, b, cones, settings)\n\nresult = Clarabel.solve!(solver)\n\nnothing #hide","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"Recover the symmetric matrix X","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"X = zeros(n,n)\nX[triu(ones(Bool,3,3))] .= result.x\nX = Symmetric(X)","category":"page"},{"location":"examples/jl/example_sdp/#Using-JuMP","page":"Julia","title":"Using JuMP","text":"","category":"section"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"We can solve the same problem a little more easily by using Clarabel.jl as the backend solver within JuMP. Here is the same problem again. Note that we are not required to model our SDP constraint in triangular form if we are using JuMP.","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"using Clarabel, JuMP\n\nn = 3\nA = [1 2 4;\n 2 3 5;\n 4 5 6]\n\nmodel = JuMP.Model(Clarabel.Optimizer)\nset_optimizer_attribute(model, \"verbose\", true)\nset_optimizer_attribute(model, \"equilibrate_enable\",false)\n\n@variable(model, X[1:n,1:n],PSD)\n@constraint(model, tr(A*X) == 1)\n@objective(model, Min, tr(X))\n\noptimize!(model)","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"Here is the solution again","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"JuMP.value.(X)","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"","category":"page"},{"location":"examples/jl/example_sdp/","page":"Julia","title":"Julia","text":"This page was generated using Literate.jl.","category":"page"},{"location":"examples/rs/example_expcone/","page":"Rust","title":"Rust","text":"Complete Cargo projects for all Rust examples can be found in examples/rs.","category":"page"},{"location":"examples/rs/example_expcone/","page":"Rust","title":"Rust","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/rs/example_expcone/src/main.rs\",\n language = :rust)","category":"page"},{"location":"examples/rs/example_sdp/","page":"Rust","title":"Rust","text":"Complete Cargo projects for all Rust examples can be found in examples/rs.","category":"page"},{"location":"examples/rs/example_sdp/","page":"Rust","title":"Rust","text":"using Documenter\nDocumenter.md_include(\n source = \"examples/rs/example_sdp/src/main.rs\",\n language = :rust)","category":"page"}] +} diff --git a/v0.8.0/siteinfo.js b/v0.8.0/siteinfo.js new file mode 100644 index 0000000..9d15fd0 --- /dev/null +++ b/v0.8.0/siteinfo.js @@ -0,0 +1 @@ +var DOCUMENTER_CURRENT_VERSION = "v0.8.0"; diff --git a/v0.8.0/user_guide_c_cpp/index.html b/v0.8.0/user_guide_c_cpp/index.html new file mode 100644 index 0000000..e175429 --- /dev/null +++ b/v0.8.0/user_guide_c_cpp/index.html @@ -0,0 +1,6 @@ + +C/C++ · Clarabel jl/rs
GitHub
diff --git a/v0.8.0/user_guide_chordal/index.html b/v0.8.0/user_guide_chordal/index.html new file mode 100644 index 0000000..7e19827 --- /dev/null +++ b/v0.8.0/user_guide_chordal/index.html @@ -0,0 +1,6 @@ + +Chordal Decomposition · Clarabel jl/rs
GitHub

Chordal Decomposition

Clarabel implements a chordal decomposition and clique merging method to solve large-scale semidefinite programming problems. If the problem has favorable structure, this method can decompose a sparse positive semidefiniteness constraint on a large semidefinite cone into a collection of semidefinite constraints on a collection of smaller cones. This can lead to significant computational savings in terms of both memory and time.

Clarabel uses the same decomposition strategy as COSMO.jl. For details see our paper on clique merging techniques and this presentation by Michael Garstka.

diff --git a/v0.8.0/user_guide_r/index.html b/v0.8.0/user_guide_r/index.html new file mode 100644 index 0000000..c7f263d --- /dev/null +++ b/v0.8.0/user_guide_r/index.html @@ -0,0 +1,6 @@ + +R · Clarabel jl/rs
GitHub