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Documenter.jl committed Sep 10, 2023
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4 changes: 2 additions & 2 deletions dev/constraints/index.html
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36 changes: 18 additions & 18 deletions dev/generated/Extension/certificate.ipynb
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Expand Up @@ -112,15 +112,15 @@
"name": "stdout",
"output_type": "stream",
"text": [
"Iter: 10 Ap: 9.69e-01 Pobj: -1.0000000e+00 Ad: 9.69e-01 Dobj: -1.0000000e+00 \n",
"Iter: 9 Ap: 9.68e-01 Pobj: -1.0000000e+00 Ad: 1.00e+00 Dobj: -1.0000000e+00 \n",
"Success: SDP solved\n",
"Primal objective value: -1.0000000e+00 \n",
"Dual objective value: -1.0000000e+00 \n",
"Relative primal infeasibility: 1.04e-15 \n",
"Relative dual infeasibility: 6.69e-10 \n",
"Real Relative Gap: -3.43e-10 \n",
"XZ Relative Gap: 1.28e-09 \n",
"DIMACS error measures: 1.99e-15 0.00e+00 1.59e-09 0.00e+00 -3.43e-10 1.28e-09\n",
"Relative primal infeasibility: 7.80e-16 \n",
"Relative dual infeasibility: 7.52e-09 \n",
"Real Relative Gap: -9.81e-09 \n",
"XZ Relative Gap: 6.28e-09 \n",
"DIMACS error measures: 1.49e-15 0.00e+00 1.79e-08 0.00e+00 -9.81e-09 6.28e-09\n",
"------------------------------------------------------------------\n",
"\t SCS v3.2.3 - Splitting Conic Solver\n",
"\t(c) Brendan O'Donoghue, Stanford University, 2012\n",
Expand All @@ -138,12 +138,12 @@
"------------------------------------------------------------------\n",
" iter | pri res | dua res | gap | obj | scale | time (s)\n",
"------------------------------------------------------------------\n",
" 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.43e-04 \n",
" 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 3.10e-04 \n",
" 0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.21e-04 \n",
" 25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 2.94e-04 \n",
"------------------------------------------------------------------\n",
"status: unbounded\n",
"timings: total: 3.12e-04s = setup: 8.46e-05s + solve: 2.27e-04s\n",
"\t lin-sys: 1.68e-05s, cones: 1.73e-04s, accel: 2.00e-06s\n",
"timings: total: 2.96e-04s = setup: 7.84e-05s + solve: 2.17e-04s\n",
"\t lin-sys: 1.45e-05s, cones: 1.69e-04s, accel: 2.20e-06s\n",
"------------------------------------------------------------------\n",
"objective = -inf\n",
"------------------------------------------------------------------\n"
Expand Down Expand Up @@ -173,7 +173,7 @@
{
"output_type": "execute_result",
"data": {
"text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : INFEASIBLE\n Message from the solver:\n \"unbounded\"\n\n* Candidate solution (result #1)\n Primal status : INFEASIBLE_POINT\n Dual status : INFEASIBILITY_CERTIFICATE\n Objective value : NaN\n Dual objective value : -1.00000e+00\n\n* Work counters\n Solve time (sec) : 3.12001e-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) : 2.95705e-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 2.65e-04 \n",
" 250| 1.40e-03 5.14e-05 7.85e-06 8.28e-01 1.00e-01 4.58e-03 \n",
" 0| 8.53e+00 5.66e-01 3.99e+01 -2.00e+01 1.00e-01 3.03e-04 \n",
" 250| 1.40e-03 5.14e-05 7.85e-06 8.28e-01 1.00e-01 4.67e-03 \n",
"------------------------------------------------------------------\n",
"status: solved\n",
"timings: total: 4.59e-03s = setup: 1.19e-04s + solve: 4.47e-03s\n",
"\t lin-sys: 2.53e-04s, cones: 3.99e-03s, accel: 4.84e-05s\n",
"timings: total: 4.67e-03s = setup: 1.36e-04s + solve: 4.53e-03s\n",
"\t lin-sys: 2.77e-04s, cones: 4.03e-03s, accel: 6.50e-05s\n",
"------------------------------------------------------------------\n",
"objective = 0.828440\n",
"------------------------------------------------------------------\n"
Expand All @@ -286,7 +286,7 @@
{
"output_type": "execute_result",
"data": {
"text/plain": "* Solver : Dual model with SCS attached\n\n* Status\n Result count : 1\n Termination status : OPTIMAL\n Message from the solver:\n \"solved\"\n\n* Candidate solution (result #1)\n Primal status : FEASIBLE_POINT\n Dual status : FEASIBLE_POINT\n Objective value : 8.28436e-01\n Dual objective value : 8.28444e-01\n\n* Work counters\n Solve time (sec) : 4.58541e-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) : 4.66857e-03\n"
},
"metadata": {},
"execution_count": 6
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"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.2"
"version": "1.9.3"
},
"kernelspec": {
"name": "julia-1.9",
"display_name": "Julia 1.9.2",
"display_name": "Julia 1.9.3",
"language": "julia"
}
},
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1 change: 0 additions & 1 deletion dev/generated/Extension/certificate.jl
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Expand Up @@ -68,4 +68,3 @@ optimize!(model)
solution_summary(model)

# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl

18 changes: 9 additions & 9 deletions dev/generated/Extension/certificate/index.html
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optimize!(model)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Success: SDP solved
Primal objective value: 0.0000000e+00
Dual objective value: 0.0000000e+00
Relative primal infeasibility: 4.15e-17
Relative primal infeasibility: 0.00e+00
Relative dual infeasibility: 5.00e-11
Real Relative Gap: 0.00e+00
XZ Relative Gap: 3.63e-10
DIMACS error measures: 6.34e-17 0.00e+00 5.00e-11 0.00e+00 0.00e+00 3.63e-10
DIMACS error measures: 0.00e+00 0.00e+00 5.00e-11 0.00e+00 0.00e+00 3.63e-10
------------------------------------------------------------------
SCS v3.2.3 - Splitting Conic Solver
(c) Brendan O&#39;Donoghue, Stanford University, 2012
Expand All @@ -39,12 +39,12 @@
------------------------------------------------------------------
iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 2.45e-04
25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 4.13e-04
0| 2.57e+01 1.01e+00 2.00e+06 -1.00e+06 1.00e-01 1.44e-04
25| 1.30e+11 4.45e+10 8.00e+18 -4.00e+18 1.00e-01 3.11e-04
------------------------------------------------------------------
status: unbounded
timings: total: 4.15e-04s = setup: 1.53e-04s + solve: 2.61e-04s
lin-sys: 1.74e-05s, cones: 2.02e-04s, accel: 1.60e-06s
timings: total: 3.12e-04s = setup: 8.90e-05s + solve: 2.23e-04s
lin-sys: 1.45e-05s, cones: 1.77e-04s, accel: 1.90e-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
Expand All @@ -62,7 +62,7 @@
Dual objective value : -1.00000e+00

* Work counters
Solve time (sec) : 4.14600e-04
Solve time (sec) : 3.12105e-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
Expand Down Expand Up @@ -125,5 +125,5 @@
Dual objective value : 8.28444e-01

* Work counters
Solve time (sec) : 4.58770e-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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 25 July 2023 16:23">Tuesday 25 July 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
Solve time (sec) : 4.53727e-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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 10 September 2023 07:32">Sunday 10 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
12 changes: 6 additions & 6 deletions dev/generated/Extension/hypercube.ipynb
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"output_type": "stream",
"text": [
"termination_status(model) = MathOptInterface.OPTIMAL\n",
"objective_value(model) = -4.404406006575101e-10\n"
"objective_value(model) = -4.1458531052640524e-10\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "-4.404406006575101e-10"
"text/plain": "-4.1458531052640524e-10"
},
"metadata": {},
"execution_count": 2
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"output_type": "stream",
"text": [
"termination_status(model) = MathOptInterface.OPTIMAL\n",
"objective_value(model) = -4.404406006575101e-10\n"
"objective_value(model) = -4.1458531052640524e-10\n"
]
},
{
"output_type": "execute_result",
"data": {
"text/plain": "-4.404406006575101e-10"
"text/plain": "-4.1458531052640524e-10"
},
"metadata": {},
"execution_count": 4
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"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.9.2"
"version": "1.9.3"
},
"kernelspec": {
"name": "julia-1.9",
"display_name": "Julia 1.9.2",
"display_name": "Julia 1.9.3",
"language": "julia"
}
},
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1 change: 0 additions & 1 deletion dev/generated/Extension/hypercube.jl
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Expand Up @@ -66,4 +66,3 @@ min_algebraic_rational(H, 0)
min_algebraic_rational(H, 1)

# This file was generated using Literate.jl, https://github.com/fredrikekre/Literate.jl

6 changes: 3 additions & 3 deletions dev/generated/Extension/hypercube/index.html
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@show objective_value(model)
end

min_algebraic(S)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-4.404406006575101e-10</code></pre><p>Note that the minimum is in fact <code>1</code>. Indeed, since each variables is odd (it is either <code>-1</code> or <code>1</code>) and there is an odd number of variables, their sum is odd. Therefore it cannot be zero!</p><p>We can see that the Gröbner basis of <code>S</code> was computed</p><pre><code class="language-julia hljs">@show S.I.gröbner_basis
min_algebraic(S)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-4.1458531052640524e-10</code></pre><p>Note that the minimum is in fact <code>1</code>. Indeed, since each variables is odd (it is either <code>-1</code> or <code>1</code>) and there is an odd number of variables, their sum is odd. Therefore it cannot be zero!</p><p>We can see that the Gröbner basis of <code>S</code> was computed</p><pre><code class="language-julia hljs">@show S.I.gröbner_basis
S.I.algo</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">Buchberger(1.4901161193847656e-8, SemialgebraicSets.presort!, SemialgebraicSets.normal_selection)</code></pre><p>The Gröbner basis is simple to compute in this case as the vector of <code>xi^2 - 1</code> is already a Gröbner basis. However, we still need to divide polynomials by the Gröbner basis which can be simplified in this case.</p><pre><code class="language-julia hljs">const MP = MultivariatePolynomials
const SS = SemialgebraicSets
struct HypercubeIdeal{V} &lt;: SS.AbstractPolynomialIdeal
Expand Down Expand Up @@ -49,11 +49,11 @@

H = HypercubeSet(HypercubeIdeal(x))

min_algebraic(H)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-4.404406006575101e-10</code></pre><p>Let&#39;s now try to find the correct lower bound:</p><pre><code class="language-julia hljs">function min_algebraic_rational(S, d)
min_algebraic(H)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-4.1458531052640524e-10</code></pre><p>Let&#39;s now try to find the correct lower bound:</p><pre><code class="language-julia hljs">function min_algebraic_rational(S, d)
model = SOSModel(solver)
@variable(model, q, SOSPoly(MP.monomials(x, 0:d)))
deno = q + 1
@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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 25 July 2023 16:23">Tuesday 25 July 2023</span>. Using Julia version 1.9.2.</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 10 September 2023 07:32">Sunday 10 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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