-opt,sol,data = complex_cs_tssos_first(pop, z, order, numeq=3, TS="block", solution=true)</code></pre><h3 id="Keyword-arguments"><a class="docs-heading-anchor" href="#Keyword-arguments">Keyword arguments</a><a id="Keyword-arguments-1"></a><a class="docs-heading-anchor-permalink" href="#Keyword-arguments" title="Permalink"></a></h3><table><tr><th style="text-align: right">Argument</th><th style="text-align: left">Description</th><th style="text-align: left">Default value</th></tr><tr><td style="text-align: right">nb</td><td style="text-align: left">Specify the first <strong>nb</strong> complex variables to be of unit norm</td><td style="text-align: left">0</td></tr><tr><td style="text-align: right">numeq</td><td style="text-align: left">Specify the last <strong>numeq</strong> constraints to be equality constraints</td><td style="text-align: left">0</td></tr><tr><td style="text-align: right">CS</td><td style="text-align: left">Types of chordal extensions in exploiting correlative sparsity: "MF" (approximately smallest chordal extension), "NC" (not performing chordal extension), false (invalidating correlative sparsity exploitation)</td><td style="text-align: left">"MF"</td></tr><tr><td style="text-align: right">cliques</td><td style="text-align: left">Use customized variable cliques</td><td style="text-align: left">[]</td></tr><tr><td style="text-align: right">TS</td><td style="text-align: left">Types of chordal extensions used in term sparsity iterations: "block"(maximal chordal extension), "MD" (approximately smallest chordal extension), false (invalidating term sparsity iterations)</td><td style="text-align: left">"block"</td></tr><tr><td style="text-align: right">ConjugateBasis</td><td style="text-align: left">include conjugate variables in monomial bases</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">normality</td><td style="text-align: left">Impose normality condtions of order <strong>normality</strong></td><td style="text-align: left">1</td></tr><tr><td style="text-align: right">merge</td><td style="text-align: left">Merge overlapping PSD blocks</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">md</td><td style="text-align: left">Parameter for tunning the merging strength</td><td style="text-align: left">3</td></tr><tr><td style="text-align: right">MomentOne</td><td style="text-align: left">add a first-order moment PSD constraint for each variable clique</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">solver</td><td style="text-align: left">Specify an SDP solver: "Mosek" or "COSMO"</td><td style="text-align: left">"Mosek"</td></tr><tr><td style="text-align: right">cosmo_setting</td><td style="text-align: left">Parameters for the COSMO solver: cosmo_para(eps_abs, eps_rel, max_iter, time_limit)</td><td style="text-align: left">cosmo_para(1e-5, 1e-5, 1e4, 0)</td></tr><tr><td style="text-align: right">mosek_setting</td><td style="text-align: left">Parameters for the Mosek solver: mosek_para(tol_pfeas, tol_dfeas, tol_relgap, time_limit, num_threads)</td><td style="text-align: left">mosek_para(1e-8, 1e-8, 1e-8, -1, 0)</td></tr><tr><td style="text-align: right">QUIET</td><td style="text-align: left">Silence the output</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">solve</td><td style="text-align: left">Solve the SDP relaxation</td><td style="text-align: left">true</td></tr><tr><td style="text-align: right">dualize</td><td style="text-align: left">Solve the dual SDP problem</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">Gram</td><td style="text-align: left">Output Gram matrices</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">solution</td><td style="text-align: left">Extract an optimal solution</td><td style="text-align: left">false</td></tr><tr><td style="text-align: right">rtol</td><td style="text-align: left">tolerance for rank</td><td style="text-align: left">1e-2</td></tr><tr><td style="text-align: right">gtol</td><td style="text-align: left">tolerance for global optimality gap</td><td style="text-align: left">1e-2</td></tr><tr><td style="text-align: right">ftol</td><td style="text-align: left">tolerance for feasibility</td><td style="text-align: left">1e-3</td></tr></table><h3 id="References"><a class="docs-heading-anchor" href="#References">References</a><a id="References-1"></a><a class="docs-heading-anchor-permalink" href="#References" title="Permalink"></a></h3><ol><li><a href="https://link.springer.com/article/10.1007/s10957-021-01975-z">Exploiting Sparsity in Complex Polynomial Optimization</a>, Jie Wang and Victor Magron, 2021.</li></ol></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../pmo/">« Polynomial Matrix Optimization</a><a class="docs-footer-nextpage" href="../opf/">AC Optimal Power Flow »</a><div class="flexbox-break"></div><p 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