Тип публикации: статья из журнала
Год издания: 2023
Идентификатор DOI: 10.3390/math11102264
Ключевые слова: minimization method, relaxation subgradients method, conjugate subgradients, Kaczmarzalgorithm
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 (witПоказать полностьюh 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.
Журнал: Mathematics
Выпуск журнала: Т. 11, № 10
Номера страниц: 2264
ISSN журнала: 22277390