About some works of Boris Polyak on convergence of gradient methods and their development
arxiv(2023)
摘要
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.
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