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<section id="autolyap">
<h1>AutoLyap<a class="headerlink" href="#autolyap" title="Link to this heading"></a></h1>
<p>A Python package for automated Lyapunov-based convergence analyses of first-order optimization and inclusion methods.</p>
<hr class="docutils" />
<section id="overview">
<h2>Overview<a class="headerlink" href="#overview" title="Link to this heading"></a></h2>
<p>AutoLyap streamlines the process of constructing and verifying Lyapunov analyses by formulating them as semidefinite programs (SDPs). It supports a broad class of structured optimization and inclusion problems, providing computer-assisted proofs of linear or sublinear convergence rates for many well‑known algorithms.</p>
<p>A typical workflow:</p>
<ol class="arabic simple">
<li><p>Choose the class of optimization/inclusion problems.</p></li>
<li><p>Choose the first-order method to analyze.</p></li>
<li><p>Choose the type of Lyapunov analysis to search for or verify (which implies a convergence or performance conclusion).</p></li>
</ol>
<p>AutoLyap builds the underlying SDP and solves it through configurable backend
solvers.</p>
</section>
<section id="quick-start">
<h2>Quick start<a class="headerlink" href="#quick-start" title="Link to this heading"></a></h2>
<p>For installation instructions and first end-to-end workflows, see
<a class="reference internal" href="quick_start/"><span class="doc">Quick start</span></a>.</p>
</section>
<section id="cite-this-project">
<h2>Cite this project<a class="headerlink" href="#cite-this-project" title="Link to this heading"></a></h2>
<p>If AutoLyap contributes to your research or software, please cite
<span id="id1">[<a class="reference internal" href="#id203" title="Manu Upadhyaya, Shuvomoy Das Gupta, Adrien B. Taylor, Sebastian Banert, and Pontus Giselsson. The AutoLyap software suite for computer-assisted Lyapunov analyses of first-order methods. 2026. arXiv:2506.24076.">UDGT+26</a>]</span>.</p>
<div class="highlight-bibtex notranslate"><div class="highlight"><pre><span></span><span class="nc">@misc</span><span class="p">{</span><span class="nl">upadhyaya2026autolyap</span><span class="p">,</span>
<span class="w"> </span><span class="na">author</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{Upadhyaya, Manu and Das Gupta, Shuvomoy and Taylor, Adrien B. and Banert, Sebastian and Giselsson, Pontus}</span><span class="p">,</span>
<span class="w"> </span><span class="na">title</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{The {AutoLyap} software suite for computer-assisted {L}yapunov analyses of first-order methods}</span><span class="p">,</span>
<span class="w"> </span><span class="na">year</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{2026}</span><span class="p">,</span>
<span class="w"> </span><span class="na">archivePrefix</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{arXiv}</span><span class="p">,</span>
<span class="w"> </span><span class="na">eprint</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{2506.24076}</span><span class="p">,</span>
<span class="w"> </span><span class="na">primaryClass</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">{math.OC}</span><span class="p">,</span>
<span class="p">}</span>
</pre></div>
</div>
<div class="docutils container" id="id2">
<div role="list" class="citation-list">
<div class="citation" id="id203" role="doc-biblioentry">
<span class="label"><span class="fn-bracket">[</span><a role="doc-backlink" href="#id1">UDGT+26</a><span class="fn-bracket">]</span></span>
<p>Manu Upadhyaya, Shuvomoy Das Gupta, Adrien B. Taylor, Sebastian Banert, and Pontus Giselsson. The AutoLyap software suite for computer-assisted Lyapunov analyses of first-order methods. 2026. <a class="reference external" href="https://arxiv.org/abs/2506.24076">arXiv:2506.24076</a>.</p>
</div>
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</section>
<section id="other-computer-assisted-methodologies">
<h2>Other computer-assisted methodologies<a class="headerlink" href="#other-computer-assisted-methodologies" title="Link to this heading"></a></h2>
<p><a class="reference external" href="https://pepit.readthedocs.io">PEPit</a> is a computer-assisted performance estimation framework that targets worst-case analyses of first-order methods through SDP formulations. AutoLyap is complementary: it focuses on Lyapunov analyses and automates the corresponding SDP formulations. In practice, PEPit is a strong choice for tight bounds, while AutoLyap is tailored to Lyapunov-based proofs and scalable analysis patterns.</p>
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