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{"documenter":{"julia_version":"1.7.3","generation_timestamp":"2024-05-22T06:20:26","documenter_version":"1.4.1"}}
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Description</a></li><li><a class="tocitem" href="../../examples/jl/example_powcone/">Julia</a></li><li><a class="tocitem" href="../../examples/rs/example_powcone/">Rust</a></li><li><a class="tocitem" href="../../examples/py/example_powcone/">Python</a></li></ul></li><li><input class="collapse-toggle" id="menuitem-3-5" type="checkbox"/><label class="tocitem" for="menuitem-3-5"><span class="docs-label">Semidefinite Program (SDP)</span><i class="docs-chevron"></i></label><ul class="collapsed"><li><a class="tocitem" href="../../examples/example_sdp/">Problem Description</a></li><li><a class="tocitem" href="../../examples/jl/example_sdp/">Julia</a></li><li><a class="tocitem" href="../../examples/rs/example_sdp/">Rust</a></li><li><a class="tocitem" href="../../examples/py/example_sdp/">Python</a></li></ul></li></ul></li><li><a class="tocitem" href="../../citing/">Citing Clarabel</a></li><li><a class="tocitem" href="../../contributing/">Contributing</a></li><li><span class="tocitem">API Reference</span><ul><li><a class="tocitem" href="../../api_cone_types/">Supported Cone Types</a></li><li><a class="tocitem" href="../../api_settings/">Solver Settings</a></li><li><a class="tocitem" href="../../api_jl/">Julia API</a></li><li><a class="tocitem" href="../../api_rs/">Rust API ⧉</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>-</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>-</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/oxfordcontrol/ClarabelDocs" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/oxfordcontrol/ClarabelDocs/blob/main/docs/src/_common/getting_started_constraints.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><p>The Clarabel interface expects constraints to be presented in the single vectorized form <span>$Ax + s = b, s \in \mathcal{K}$</span>, where <span>$\mathcal{K} = \mathcal{K}_1 \times \dots \times \mathcal{K}_p$</span> and each <span>$\mathcal{K}_i$</span> is one of the solver&#39;s supported cone types.</p><p>Suppose that we have a problem with decision variable <span>$x \in \mathbb{R}^3$</span> and our constraints are:</p><ul><li>A single equality constraint <span>$x_1 + x_2 - x_3 = 1$</span>. </li><li>A pair of inequalities such that <span>$x_2$</span> and <span>$x_3$</span> are each less than 2.</li><li>A second order cone constraint on the 3-dimensional vector <span>$x$</span>. </li></ul><p>For the three constraints above, we have</p><p class="math-container">\[
\begin{align*}

A_{eq} &amp;=
\left[
\begin{array}{lll}
1 &amp; 1 &amp; -1
\end{array}
\right],
\quad &amp;
b_{eq} &amp;=
\left[
\begin{array}{l}
1
\end{array}
\right],

\\[4ex]

A_{ineq} &amp;=
\left[
\begin{array}{lll}
0 &amp; 1 &amp; 0 \\
0 &amp; 0 &amp; 1
\end{array}
\right],
\quad &amp;
b_{ineq} &amp;=
\left[
\begin{array}{l}
2\\2
\end{array}
\right],

\\[4ex]

A_{soc} &amp;=
\left[
\begin{array}{rrr}
-1 &amp; 0 &amp; 0 \\
0 &amp; -1 &amp; 0 \\
0 &amp; 0 &amp; -1
\end{array}
\right],
\quad &amp;
b_{soc} &amp;=
\left[
\begin{array}{l}
0 \\0 \\0
\end{array}
\right]

\end{align*}
\]</p></article><nav class="docs-footer"><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="auto">Automatic (OS)</option><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 1.4.1 on <span class="colophon-date" title="Wednesday 22 May 2024 06:20">Wednesday 22 May 2024</span>. Using Julia version 1.7.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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