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dev/.documenter-siteinfo.json

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{"documenter":{"julia_version":"1.11.5","generation_timestamp":"2025-06-24T18:08:33","documenter_version":"1.13.0"}}
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{"documenter":{"julia_version":"1.11.6","generation_timestamp":"2025-07-28T16:26:57","documenter_version":"1.14.1"}}

dev/assets/documenter.js

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dev/background/decomposition_detection/index.html

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\end{equation}\]</p><p>This is an <span>$n$</span>-dimensional box-constrained convex QP, for which there is no closed form solution. Note that by using a custom generic decomposition, L2ODLL can still be used to set up this problem and solve it using a JuMP-compatible QP solver.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../decompositions/">« Decompositions</a><a class="docs-footer-nextpage" href="../../public/">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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.13.0 on <span class="colophon-date" title="Tuesday 24 June 2025 18:08">Tuesday 24 June 2025</span>. Using Julia version 1.11.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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\end{equation}\]</p><p>This is an <span>$n$</span>-dimensional box-constrained convex QP, for which there is no closed form solution. Note that by using a custom generic decomposition, L2ODLL can still be used to set up this problem and solve it using a JuMP-compatible QP solver.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../decompositions/">« Decompositions</a><a class="docs-footer-nextpage" href="../../public/">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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.14.1 on <span class="colophon-date" title="Monday 28 July 2025 16:26">Monday 28 July 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/background/decompositions/index.html

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\end{equation}\]</p><p>This model admits a closed form solution, <span>$z = \frac{1}{2}Q^{-1}(c - A^\top y)$</span>. Furthermore, the closed form dual solution in this case is <span>$x=z$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../decomposition_detection/">Decomposition detection »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.13.0 on <span class="colophon-date" title="Tuesday 24 June 2025 18:08">Tuesday 24 June 2025</span>. Using Julia version 1.11.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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\end{equation}\]</p><p>This model admits a closed form solution, <span>$z = \frac{1}{2}Q^{-1}(c - A^\top y)$</span>. Furthermore, the closed form dual solution in this case is <span>$x=z$</span>.</p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../decomposition_detection/">Decomposition detection »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.14.1 on <span class="colophon-date" title="Monday 28 July 2025 16:26">Monday 28 July 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/index.html

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dobj = L2ODLL.dual_objective(model, y_predicted, param_value)
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dobj_wrt_y = L2ODLL.dual_objective_gradient(model, y_predicted, param_value)</code></pre><p>This also works with batches, using broadcasting:</p><pre><code class="language-julia hljs">dobj = L2ODLL.dual_objective.(model, y_predicted_batch, param_value_batch)
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dobj_wrt_y = L2ODLL.dual_objective_gradient.(model, y_predicted_batch, param_value_batch)</code></pre><div class="admonition is-warning" id="Warning-5007a2a6f53b49f6"><header class="admonition-header">Warning<a class="admonition-anchor" href="#Warning-5007a2a6f53b49f6" title="Permalink"></a></header><div class="admonition-body"><p>These functions currently run on the CPU. A batched GPU-friendly version is coming soon.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="background/decompositions/">Decompositions »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.13.0 on <span class="colophon-date" title="Tuesday 24 June 2025 18:08">Tuesday 24 June 2025</span>. Using Julia version 1.11.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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dobj_wrt_y = L2ODLL.dual_objective_gradient.(model, y_predicted_batch, param_value_batch)</code></pre><div class="admonition is-warning" id="Warning-5007a2a6f53b49f6"><header class="admonition-header">Warning<a class="admonition-anchor" href="#Warning-5007a2a6f53b49f6" title="Permalink"></a></header><div class="admonition-body"><p>These functions currently run on the CPU. A batched GPU-friendly version is coming soon.</p></div></div></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="background/decompositions/">Decompositions »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.14.1 on <span class="colophon-date" title="Monday 28 July 2025 16:26">Monday 28 July 2025</span>. Using Julia version 1.11.6.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

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