Автор(ы): Поляк Б. Т. (ИПУ РАН, Лаборатория 07)Автор(ов): 1 Параметры публикацииТип публикации: Тезисы докладаНазвание: Randomized Methods for Convex OptimizationНаименование конференции: Nonlinear Analysis and Оptimization ProblemsГород: -Издательство: -Год издания: 2008Страницы: - АннотацияRandomized methods play significant role in optimization and control and in many situations can be competitors with deterministic algorithms. We consider general convex optimization problem in Rn and assume that generator of uniformly distributed points in a convex set is available. After generation of N such points the best of them is used to make a cut of the admissible set, and the process is continued in the remaining body. The expected rate of convergence is estimated, it is geometric with denominator depending on N and n. For N=1 the result coincides with Radon theorem on center of gravity of a convex body. To implement such method one should approximate random uniform generator. It can be done by use of modern Markov–chain Monte Carlo techniques such as Hit–and–Run and Shake–and–Bake. The results of numerical simulation for solving Semi Definite Programming problems will be presented. They include large dimensional problems, for instance LMIs with 100x100 matrix variables. Библиографическая ссылка: Поляк Б.Т. Randomized Methods for Convex Optimization / . -: -, 2008. С. -.