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

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Subgradient method Maxima and minima Gradient method Convergence (economics) Function (biology) Mathematical optimization Convex function Mathematics Regular polygon Applied mathematics Computer science Mathematical analysis Economics Geometry Evolutionary biology Economic growth Biology

Seydamet Ablaev , Aleksandr Beznosikov , Alexander Gasnikov , Darina Dvinskikh , A. V. Lobanov , S. M. Puchinin , Fedor Stonyakin ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2311.16743 · OA: W4389156919

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.