arXiv subjects

Seydamet Ablaev

Publications and source records attributed to Seydamet Ablaev.

2 recordsLinked to original sources

arXiv2024

About some works of Boris Polyak on convergence of gradient methods and their development

The paper presents a review of the state-of-the-art of subgradient and accelerated methods of convex optimization, including in the presence of disturbances and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polak-Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of sharp minima is considered. The purpose of this survey is to show the influence of the works of B.T. Polyak (1935 -- 2023) on gradient optimization methods and their neighborhoods on the modern development of numerical optimization methods.

math.OC↗

arXiv2021

Analogues of Switching Subgradient Schemes for Relatively Lipschitz-Continuous Convex Programming Problems

Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective function and functional constraints. We introduce a new concept of an inexact model and propose some analogues of switching subgradient schemes for convex programming problems for the relatively Lipschitz-continuous objective function and functional constraints. Some class of online convex optimization problems is considered. The proposed methods are optimal in the class of optimization problems with relatively Lipschitz-continuous objective and functional constraints.

math.OC↗