On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development
Pub Date : 2024-06-07
DOI:10.1134/s0965542524700076
引用次数: 0
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.
论鲍里斯-捷奥多罗维奇-波利亚克关于梯度法收敛及其发展的一些著作
摘要 本文综述了亚梯度和加速凸优化方法的现状，包括存在噪声和获取目标函数各种信息（函数值、梯度、随机梯度、高导数）的情况。对于非凸问题，考虑了 Polyak-Lojasiewicz 条件，并对主要结果进行了综述。还考虑了数值方法在出现急剧最小值时的行为。本综述旨在说明 B.T. Polyak（1935-2023 年）的梯度优化方法及其周围环境对现代数值优化方法发展的影响。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
求助全文
约1分钟内获得全文
求助全文
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
