Numerical Optimization

<!DOCTYPE HTML>  <html> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8"/> <link href="http://fonts.googleapis.com/css?family=Oswald|Lobster|Average" rel="stylesheet" type="text/css" /> <title>Numerical Optimization</title> <meta charset="utf-8" /> <meta name="viewport" content="width=device-width, initial-scale=1, user-scalable=no" /> <link rel="stylesheet" href="assets/css/main.css" /> <script> (function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) })(window,document,'script','https://www.google-analytics.com/analytics.js','ga'); ga('create', 'UA-16599435-5', 'auto'); ga('send', 'pageview'); </script> </head> <body class="is-preload">  <div id="content"> <div class="inner">  <article class="box post post-excerpt"> <header>  <div class="container"> <div class="text"> <h1>Numerical Optimization</h1><br> <p> Teacher: <a href="index.html">Alberto Bemporad</a> </p> </div> <div class="image"> <img src="images/blackboard.png"> </div> </div> </header> <p><strong>Course description</strong></p> <p> Optimization plays a key role in solving a large variety of decision problems that arise in engineering (design, process operations, embedded systems), data science, machine learning, business analytics, finance, economics, and many others. This course focuses on formulating optimization models and on the most popular numerical methods to solve them. </p> <p><strong>Syllabus</strong></p> <p> Modeling: linear programming models, convex optimization models. Basic optimization theory: optimality conditions, sensitivity, duality. Algorithms for constrained convex optimization: active-set methods for linear and quadratic programming, proximal methods and ADMM, stochastic gradient, interior-point methods. Line-search methods for unconstrained nonlinear programming, sequential quadratic programming. </p> <p><strong>Prerequisites</strong></p> <p> Linear algebra and matrix computation, calculus and mathematical analysis. </p> <p><strong>Timetable</strong></p> <table> <tr> <th>Monday</th> <th>November 25, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Wednesday</th> <th>November 27, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Friday</th> <th>November 29, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Monday</th> <th>December 2, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Wednesday</th> <th>December 4, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Friday</th> <th>December 6, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Monday</th> <th>December 9, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Tuesday</th> <th>December 10, 2024</th> <th>14:00-16:00</th> </tr> <tr> <th>Wednesday</th> <th>December 11, 2024</th> <th>09:00-11:00</th> </tr> <tr> <th>Friday</th> <th>December 13, 2024</th> <th>09:00-11:00</th> </tr> </table><p><strong>Location</strong></p> <p>Hybrid mode: IMT School, Piazza San Francesco, 19 - Lucca / Online.  </p> <p><strong>Lecture slides</strong></p> <table> <tr> <th> <a href="teaching/numopt/1-optimization_models.pdf"> Optimization models, linear and convex programming</a> </th><th>(updated 5/12/2024)</th> </tr><tr> <th><a href="teaching/numopt/2-optimality_duality.pdf"> Optimization theory (optimality conditions, duality)</a> </th><th>(updated 6/12/2024)</th> </tr><tr> <th> <a href="teaching/numopt/3-basics_linear_algebra.pdf"> Basics of numerical linear algebra</a> </th><th>(updated 11/11/2024)</th> </tr><tr> <th> <a href="teaching/numopt/4-active_set.pdf"> Active-set methods</a> </th><th>(updated 11/11/2024)</th> </tr><tr> <th> <a href="teaching/numopt/5-operator_splitting_sgd.pdf"> Operator splitting methods (proximal gradient, ADMM), stochastic gradient descent</a> </th><th>(updated 11/12/2024)</th> </tr><tr> <th> <a href="teaching/numopt/6-nonlinear_programming_ip.pdf"> Unconstrained nonlinear optimization, interior-point methods</a> </th><th>(updated 14/12/2024)</th> </th> </tr> </table> </article> </div> </div>  <div id="sidebar">  <h1 id="logo"><a href="#"></a></h1>  <nav id="nav"> <ul> <li><a href="index.html">Home</a></li> <li><a href="http://cse.lab.imtlucca.it/~bemporad/publications/">Publications</a></li> <li><a href="software.html">Software</a></li> <li><a href="teaching.html">Teaching</a></li> <li><a href="talks.html">Talks</a></li> <li><a href="projects.html">Projects</a></li> <li><a href="events.html">Events</a></li> <li><a href="biography.html">About me</a></li> </ul> </nav>  <ul id="copyright"> <li>© A. Bemporad, 2022.</li><li>Web template: <a href="http://html5up.net">HTML5 UP</a></li> </ul> </div>  <script src="assets/js/jquery.min.js"></script> <script src="assets/js/browser.min.js"></script> <script src="assets/js/breakpoints.min.js"></script> <script src="assets/js/util.js"></script> <script src="assets/js/main.js"></script> </body> </html>

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Numerical Optimization