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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta http-equiv="Content-Style-Type" content="text/css" />
<meta name="generator" content="pandoc" />
<title></title>
<style type="text/css">code{white-space: pre;}</style>
<link rel="stylesheet" href="GitHub2.css" type="text/css" />
<script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS_CHTML-full" type="text/javascript"></script>
</head>
<body>
<p><a href="https://github.com/mforets/ocrg">Link to the webpage of the repository.</a></p>
<h2 id="exercises-and-solutions-on-convex-optimization">Exercises and Solutions on Convex Optimization</h2>
<table>
<thead>
<tr class="header">
<th align="center">Exercise #</th>
<th align="center">Main topics</th>
<th align="center">Source</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><a href="./exercises_opt/BV/2-7.html">1</a></td>
<td align="center">convex set</td>
<td align="center">[BV]</td>
</tr>
<tr class="even">
<td align="center"><a href="./exercises_opt/BV_Add/1-1-ad.html">2</a></td>
<td align="center">convex set</td>
<td align="center">[BVAdd]</td>
</tr>
</tbody>
</table>
<h3 id="notation">Notation</h3>
<p>The standard notation for polynomials with coefficients on a field <span class="math inline">\(\mathbb{K}\)</span>, on a scalar (real) variable <span class="math inline">\(t\)</span>, is <span class="math inline">\(p(t) \in \mathbb{K}[t]\)</span>. Moreover, for polynomials with domain in <span class="math inline">\(\mathbb{R}^n\)</span>, we denote <span class="math inline">\(p(x) \in \mathbb{K}^n[x]\)</span>.</p>
<h2 id="notes-on-convex-optimization">Notes on Convex Optimization</h2>
<p>These notes are mainly from the book by Boyd and Vandenberghe [BV].</p>
<table style="width:78%;">
<colgroup>
<col width="16%" />
<col width="61%" />
</colgroup>
<thead>
<tr class="header">
<th align="center">Chapter</th>
<th align="center">Main topics</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="center"><a href="./notes-eng/convex-sets.html">Convex sets</a>, <a href="./notes-eng/convex-sets-sl.html">slideshow</a></td>
<td align="center">definition of convexity; operations that preserve convexity; basic classes of convex sets: polyhedra, cones (proper cones, dual cones); generalized inequalities</td>
</tr>
<tr class="even">
<td align="center"><a href="./notes-eng/convex-functions.html">Convex functions</a>, <a href="./notes-eng/convex-functions-sl.html">slideshow</a></td>
<td align="center">convex functions</td>
</tr>
</tbody>
</table>
<h2 id="how-to-contribute">How to contribute</h2>
<p>If you would like to contribute with an exercise please <a href="marcelo-forets.fr">send me an email</a> and I will upload it here. Otherwise you can directly do it yourself, you just need a <a href="https://github.com/">github</a> account (it is free).</p>
<p>To actually create new content, you can do it in any text editor and save the file in .md (<a href="https://en.wikipedia.org/wiki/Markdown">Markdown</a>) format. There exist as well several programs specially conceived to formatting in Markdown. On a personal note, my favorite (for MacOS) is the open-source project <a href="macdown.uranusjr.com/">MacDown</a>.</p>
<p>If you enjoy working online, check <a href="https://stackedit.io">stack edit</a>.</p>
<h2 id="references">References:</h2>
<ul>
<li><p><strong>[BVAdd]</strong> <a href="https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf">Convex Optimization.</a>. Boyd and Vandenberghe.</p></li>
<li><p><strong>[BV]</strong> <a href="https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook_extra_exercises.pdf">Additional exercises for Convex Optimization.</a> Boyd and Vandenberghe. Aug' 2016.</p></li>
</ul>
</body>
</html>