Автор(ы): Поляк Б. Т. (ИПУ РАН, Лаборатория 07)Автор(ов): 1 Параметры публикацииТип публикации: Пленарный докладНазвание: Uniform Sampling by Random Walks in Convex SetsНаименование конференции: Standards and Ontologies for Functional GenomicsГород: БристольИздательство: -Год издания: 2010Страницы: - АннотацияRandomization methods are based on generation of uniformly distributed points in a convex set. For simple sets (balls, boxes, ellipsoids etc.) such points are generated explicitly. For more complicated sets so called MCMC (Markov Chain Monte–Carlo) algorithms are applied, they provide approximately uniform distributions. The typical example of MCMC is Hit–and–Run (H&R) method. We describe application of H&R for sets given by algebraic linear inequalities or linear matrix inequalities. Unfortunately the points generated by H&R are far from uniformly distributed for ill–shaped sets (with large ratio of its diameter to the radius of the largest inscribed ball). To improve its behavior we propose to modify the method by use of barrier functions, which are well known in interior–point methods for convex optimization. Such versions of H&R method demonstrate much better properties than standard ones. We exploit this technique for various randomization approaches to control and optimization. Библиографическая ссылка: Поляк Б.Т. Uniform Sampling by Random Walks in Convex Sets / . Бристоль: -, 2010. С. -.