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A Family ofMulti-StepSubgradientMinimization Methods: научное издание Tovbis ElenaKrutikov VladimirStanimirović Predrag2023 год

A Family of Multi-Step Subgradient Minimization Methods : научное издание
статья из журнала

Дополнительные ссылки: eLibrary
База данных: Каталог библиотеки СФУ
Библиографическое описание: A Family of Multi-Step Subgradient Minimization Methods : научное издание / E. E. Tovbis [et al.]. - Текст : непосредственный // Mathematics. - 2023. - Т. 11, № 10. - P. 2264. - This research was funded by the Ministry of Science and Higher Education of the Russian Federation (project no.: FEFE-2023-0004). - ISSN 2227-7390, DOI 10.3390/math11102264.
Аннотация: For solving non-smooth multidimensional optimization problems, we present a family of relaxation subgradient methods (RSMs) with a built-in algorithm for finding the descent direction that forms an acute angle with all subgradients in the neighborhood of the current minimum. Minimizing the function along the opposite direction (with a minus sign) enables the algorithm to go beyond the neighborhood of the current minimum. The family of algorithms for finding the descent direction is based on solving systems of inequalities. The finite convergence of the algorithms on separable bounded sets is proved. Algorithms for solving systems of inequalities are used to organize the RSM family. On quadratic functions, the methods of the RSM family are equivalent to the conjugate gradient method (CGM). The methods are intended for solving high-dimensional problems and are studied theoretically and numerically. Examples of solving convex and non-convex smooth and non-smooth problems of large dimensions are given.
Год издания: 2023
Авторы: Tovbis Elena , Krutikov Vladimir , Stanimirović Predrag , Meshechkin Vladimir , Popov Aleksey , Kazakovtsev Lev
Источник: Mathematics
Выпуск: Т. 11, № 10
Номера страниц: 2264
Держатель оригинала документа: Kemerovo State University, Reshetnev Siberian State University of Science and Technology, Siberian Federal University, University of Nis
Количество экземпляров:
Твёрдая копия издания отсутствует в фонде библиотеки

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