https://wikicshse.ru/index.php?action=history&feed=atom&title=Optimization_Methods_2022 2026-06-06T12:13:03Z История изменений этой страницы в вики MediaWiki 1.45.3 https://wikicshse.ru/index.php?title=Optimization_Methods_2022&diff=539&oldid=prev 2022-02-14T07:55:20Z

<p>Migrated current public revision from wiki.cs.hse.ru</p> <p><b>Новая страница</b></p><div>= Abstract =<br /> <br /> The course gives a comprehensive foundation for theory, methods and algorithms of mathematical optimization. The prerequisites are <br /> linear algebra and calculus.<br /> <br /> = Learning Objectives =<br /> <br /> - Students will study the main concepts of optimization theory and develop a methodology for theoretical investigation of optimization problems.<br /> <br /> - Students will obtain an understanding of creation, effectiveness and application optimization methods and algorithms on practice.<br /> <br /> - The course will give students the possibility of solving standard and nonstandard mathematical problems connected to finding optimal solutions.<br /> <br /> = Expected Learning Outcomes =<br /> <br /> - Students should be able to classify optimization problems according to their mathematical properties.<br /> <br /> - Students should be able to perform a theoretical investigation of a given optimization problem in order to assess its complexity.<br /> <br /> - Students should be able to write down first and second-order optimality conditions.<br /> <br /> - Students should be able to provide a dual analysis of linear and convex optimization problems.<br /> <br /> - Students should be able to assess the rate of convergence of the first and second-order optimization methods.<br /> <br /> - Students should be able to solve simple optimization problems without a computer.<br /> <br /> - Students should be able to implement different optimization codes in a computer environment.<br /> <br /> - Students should be able to analyse the obtained solutions.<br /> <br /> <br /> = Course content =<br /> <br /> - Unvariate optimization: unimodal (invex) functions, golden section method, Lipschitzian optimization.<br /> <br /> - Unconstrained quadratic optimization: algebraic approach, complete characterization of stationary points, gradient method with exact line search, conjugate gradient method.<br /> <br /> - General unconstrained optimization: first and second-order optimality conditions, descent directions, steepest descent method, conjugate gradient methods, Newton method, quasi-Newton methods, inexact line search, rate of convergence.<br /> <br /> - Optimization problems with linear equality constraints: first and second-order optimality conditions, Lagrange function.<br /> <br /> - General smooth optimization problems with equality and inequality constraints: first and second-order optimality conditions, dual problems, penalty and augmented Lagrangian methods, sequential quadratic programming.<br /> <br /> - Convex optimization: optimality conditions, duality, subgradients and subdifferential, cutting planes and bundle methods, the complexity of convex optimization.<br /> <br /> - Linear programming: duality, decomposition.<br /> <br /> - Interior-point methods.<br /> <br /> = Recommended Bibliography =<br /> <br /> - Nocedal J., Wright S.J. Numerical optimization. Second Edition. Springer, 2006 <br /> <br /> - Bazaraa M. S., Sherali H.D, Shetty C. M. Nonlinear Programming: Theory and Algorithms 3rd Edition, John Wiley &amp; Sons, 2006<br /> <br /> - Beck, A. First-Order Methods in Optimization, MOS-SIAM Series on Optimization, 2017<br /> <br /> - Ben-Tal A., Arkadi Nemirovski A. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications, MOS-SIAM Series on Optimization, 2001<br /> <br /> - Nesterov Yu. Introductory Lectures on Convex Optimization, Springer US, 2004</div>

imported>NATab