SEMI-PROXIMAL POINT METHOD FOR NONSMOOTH CONVEX-CONCAVE MINIMAX OPTIMIZATION
作者机构：LSECICMSECAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesDalian University of TechnologyDalian 116024China
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2024年第42卷第3期
页 面：617-637页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：supported by the Natural Science Foundation of China(Grant Nos.11991021,11991020,12021001,11971372,11971089,11731013) by the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA27000000) by the National Key R&D Program of China(Grant Nos.2021YFA1000300,2021YFA1000301)
主 题：Minimax optimization Convexity-concavity Global convergence Rate of con-vergence Locally metrical subregularity
摘 要：Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research *** there have been many numerical algorithms for solving smooth convex-concave minimax problems,numerical algorithms for nonsmooth convex-concave minimax problems are *** paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem.A semi-proximal point method(SPP)is proposed,in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each *** construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly *** prove the global convergence of our algorithm under mild assumptions,without requiring strong convexity-concavity *** the locally metrical subregularity of the solution mapping,we prove that our algorithm has the linear rate of *** numerical results are reported to verify the efficiency of our algorithm.
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