Work

On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development

Year: 2024

Type: article

Abstract: The paper presents a review of the current state of subgradient and accelerated convex optimization methods, including the cases with the presence of noise and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polyak–Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of a sharp minimum is considered. The aim of this review is to show the influence of the works of B.T. Polyak (1935–2023) on gradient optimization methods and their surroundings on the modern development of numerical optimization methods.

Source: Журнал вычислительной математики и математической физики

DOI: 10.31857/s0044466924040028

Authors: S. S. Ablaev, A. N. Beznosikov, A. V. Gasnikov, D. M. Dvinskikh, A. V. Lobanov, S. M. Puchinin, F. S. Stonyakin

Institutions: Moscow Institute of Physics and Technology, V.I. Vernadsky Crimean Federal University, Russian Academy of Sciences, Institute for Information Transmission Problems, Institute for System Programming

Language: English

Topic: Optimization and Variational Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4404415986

FWCI: 0.195

Cites: 80

Cited by: 1

Related to: 10