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previews/PR182/Examples/benders/index.html

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return best_sol[1]
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end</code></pre><p>Run benders decomposition with POI</p><pre><code class="language-julia hljs">β2 = decomposed_model(; print_timer_outputs = false);
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GC.gc()
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β2 = decomposed_model();</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../example/">« Basic Examples</a><a class="docs-footer-nextpage" href="../markowitz/">Markowitz Efficient Frontier »</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="Monday 18 August 2025 01:47">Monday 18 August 2025</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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β2 = decomposed_model();</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../example/">« Basic Examples</a><a class="docs-footer-nextpage" href="../markowitz/">Markowitz Efficient Frontier »</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="Monday 18 August 2025 02:26">Monday 18 August 2025</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR182/Examples/example/index.html

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optimize!(model)
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isapprox(objective_value(model), 128/9, atol=1e-4)
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isapprox(value(x), 4/3, atol=1e-4)
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isapprox(value(y), 4/3, atol=1e-4)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../manual/">« Manual</a><a class="docs-footer-nextpage" href="../benders/">Benders Quantile Regression »</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="Monday 18 August 2025 01:47">Monday 18 August 2025</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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isapprox(value(y), 4/3, atol=1e-4)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../manual/">« Manual</a><a class="docs-footer-nextpage" href="../benders/">Benders Quantile Regression »</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="Monday 18 August 2025 02:26">Monday 18 August 2025</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

previews/PR182/Examples/markowitz/index.html

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end</code></pre><p>Plot the efficient frontier</p><pre><code class="language-julia hljs">portfolios_values = sort(portfolios_values,by=x-&gt;x[1])
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portfolios_values_matrix = hcat([[v[1],v[2]] for v in values(portfolios_values)]...)&#39;
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plot(portfolios_values_matrix[:,2],portfolios_values_matrix[:,1],legend=false,
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xlabel=&quot;Standard Deviation&quot;, ylabel = &quot;Return&quot;, title = &quot;Efficient Frontier&quot;)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../benders/">« Benders Quantile Regression</a><a class="docs-footer-nextpage" href="../../reference/">Reference »</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="Monday 18 August 2025 01:47">Monday 18 August 2025</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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xlabel=&quot;Standard Deviation&quot;, ylabel = &quot;Return&quot;, title = &quot;Efficient Frontier&quot;)</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../benders/">« Benders Quantile Regression</a><a class="docs-footer-nextpage" href="../../reference/">Reference »</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="Monday 18 August 2025 02:26">Monday 18 August 2025</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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