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Documenter.jl committed Dec 21, 2023
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2 changes: 1 addition & 1 deletion dev/.documenter-siteinfo.json
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{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-07T17:05:57","documenter_version":"1.2.1"}}
{"documenter":{"julia_version":"1.9.4","generation_timestamp":"2023-12-21T13:46:26","documenter_version":"1.2.1"}}
2 changes: 1 addition & 1 deletion dev/bibliography/index.html
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20 changes: 10 additions & 10 deletions dev/generated/Extension/certificate.ipynb
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"------------------------------------------------------------------\n",
" iter | pri res | dua res | gap | obj | scale | time (s)\n",
"------------------------------------------------------------------\n",
" 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 9.30e-05 \n",
" 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 2.07e-04 \n",
" 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 9.09e-05 \n",
" 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 2.05e-04 \n",
"------------------------------------------------------------------\n",
"status: unbounded\n",
"timings: total: 2.08e-04s = setup: 5.76e-05s + solve: 1.51e-04s\n",
"\t lin-sys: 9.80e-06s, cones: 1.15e-04s, accel: 1.36e-06s\n",
"timings: total: 2.06e-04s = setup: 5.58e-05s + solve: 1.50e-04s\n",
"\t lin-sys: 9.86e-06s, cones: 1.15e-04s, accel: 1.43e-06s\n",
"------------------------------------------------------------------\n",
"objective = -inf\n",
"------------------------------------------------------------------\n"
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{
"output_type": "execute_result",
"data": {
"text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : INFEASIBLE\n Message from the solver:\n \"unbounded\"\n\n* Candidate solution (result #1)\n Primal status : INFEASIBLE_POINT\n Dual status : INFEASIBILITY_CERTIFICATE\n Objective value : NaN\n Dual objective value : -1.00000e+00\n\n* Work counters\n Solve time (sec) : 2.08289e-04\n"
"text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : INFEASIBLE\n Message from the solver:\n \"unbounded\"\n\n* Candidate solution (result #1)\n Primal status : INFEASIBLE_POINT\n Dual status : INFEASIBILITY_CERTIFICATE\n Objective value : NaN\n Dual objective value : -1.00000e+00\n\n* Work counters\n Solve time (sec) : 2.05962e-04\n"
},
"metadata": {},
"execution_count": 4
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"------------------------------------------------------------------\n",
" iter | pri res | dua res | gap | obj | scale | time (s)\n",
"------------------------------------------------------------------\n",
" 0| 8.53e+00 5.66e-01 3.99e+01 -2.00e+01 1.00e-01 2.14e-04 \n",
" 250| 1.40e-03 5.14e-05 7.85e-06 8.28e-01 1.00e-01 4.97e-03 \n",
" 0| 8.53e+00 5.66e-01 3.99e+01 -2.00e+01 1.00e-01 1.83e-04 \n",
" 250| 1.40e-03 5.14e-05 7.85e-06 8.28e-01 1.00e-01 3.06e-03 \n",
"------------------------------------------------------------------\n",
"status: solved\n",
"timings: total: 4.97e-03s = setup: 1.07e-04s + solve: 4.86e-03s\n",
"\t lin-sys: 2.46e-04s, cones: 4.40e-03s, accel: 4.21e-05s\n",
"timings: total: 3.06e-03s = setup: 8.04e-05s + solve: 2.98e-03s\n",
"\t lin-sys: 1.67e-04s, cones: 2.66e-03s, accel: 3.06e-05s\n",
"------------------------------------------------------------------\n",
"objective = 0.828440\n",
"------------------------------------------------------------------\n"
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{
"output_type": "execute_result",
"data": {
"text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 8.28436e-01\n Dual objective value : 8.28444e-01\n\n* Work counters\n Solve time (sec) : 4.96969e-03\n"
"text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 8.28436e-01\n Dual objective value : 8.28444e-01\n\n* Work counters\n Solve time (sec) : 3.05814e-03\n"
},
"metadata": {},
"execution_count": 6
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14 changes: 7 additions & 7 deletions dev/generated/Extension/certificate/index.html
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------------------------------------------------------------------
iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.07e-04
25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 2.27e-04
0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 9.25e-05
25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 2.06e-04
------------------------------------------------------------------
status: unbounded
timings: total: 2.28e-04s = setup: 7.10e-05s + solve: 1.57e-04s
lin-sys: 1.03e-05s, cones: 1.21e-04s, accel: 1.39e-06s
timings: total: 2.07e-04s = setup: 5.75e-05s + solve: 1.50e-04s
lin-sys: 1.01e-05s, cones: 1.15e-04s, accel: 1.36e-06s
------------------------------------------------------------------
objective = -inf
------------------------------------------------------------------</code></pre><p>We can see that the problem is infeasible, meaning that no lower bound was found.</p><pre><code class="language-julia hljs">solution_summary(model)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">* Solver : Dual model with SCS attached
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Dual objective value : -1.00000e+00

* Work counters
Solve time (sec) : 2.27895e-04
Solve time (sec) : 2.07345e-04
</code></pre><p>We now define the Schmüdgen&#39;s certificate:</p><pre><code class="language-julia hljs">import MultivariateBases as MB
const SOS = SumOfSquares
const SOSC = SOS.Certificate
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Dual objective value : 8.28444e-01

* Work counters
Solve time (sec) : 3.09675e-03
</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Symmetry/permutation_symmetry/">« Symmetry reduction</a><a class="docs-footer-nextpage" href="../hypercube/">Hypercube »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 7 December 2023 17:05">Thursday 7 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Solve time (sec) : 3.08995e-03
</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../Symmetry/permutation_symmetry/">« Symmetry reduction</a><a class="docs-footer-nextpage" href="../hypercube/">Hypercube »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 21 December 2023 13:46">Thursday 21 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/generated/Extension/hypercube/index.html
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@constraint(model, c, deno * p &gt;= deno, domain = S)
optimize!(model)
@show termination_status(model)
end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">min_algebraic_rational (generic function with 1 method)</code></pre><p>With <code>d = 0</code>, it&#39;s the same as previously</p><pre><code class="language-julia hljs">min_algebraic_rational(H, 0)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">INFEASIBLE::TerminationStatusCode = 2</code></pre><p>But with <code>d = 1</code>, we can find the correct lower bound</p><pre><code class="language-julia hljs">min_algebraic_rational(H, 1)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">OPTIMAL::TerminationStatusCode = 1</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../certificate/">« Certificate</a><a class="docs-footer-nextpage" href="../typed/">Multivariate polynomials implementations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 7 December 2023 17:05">Thursday 7 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">min_algebraic_rational (generic function with 1 method)</code></pre><p>With <code>d = 0</code>, it&#39;s the same as previously</p><pre><code class="language-julia hljs">min_algebraic_rational(H, 0)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">INFEASIBLE::TerminationStatusCode = 2</code></pre><p>But with <code>d = 1</code>, we can find the correct lower bound</p><pre><code class="language-julia hljs">min_algebraic_rational(H, 1)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">OPTIMAL::TerminationStatusCode = 1</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../certificate/">« Certificate</a><a class="docs-footer-nextpage" href="../typed/">Multivariate polynomials implementations »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Thursday 21 December 2023 13:46">Thursday 21 December 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
8 changes: 4 additions & 4 deletions dev/generated/Extension/typed.ipynb
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{
"output_type": "execute_result",
"data": {
"text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 1.45108e-01\n"
"text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 1.52004e-01\n"
},
"metadata": {},
"execution_count": 1
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"name": "stdout",
"output_type": "stream",
"text": [
" 516.264 μs (6614 allocations: 1.34 MiB)\n"
" 453.712 μs (6614 allocations: 1.34 MiB)\n"
]
},
{
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"name": "stdout",
"output_type": "stream",
"text": [
" 788.682 μs (9990 allocations: 1.26 MiB)\n"
" 699.919 μs (9990 allocations: 1.26 MiB)\n"
]
},
{
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{
"output_type": "execute_result",
"data": {
"text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 6.74330e-01\n"
"text/plain": "* Solver : CSDP\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"Problem solved to optimality.\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 0.00000e+00\n Dual objective value : 0.00000e+00\n\n* Work counters\n Solve time (sec) : 6.03909e-01\n"
},
"metadata": {},
"execution_count": 5
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