Year: 2024
Author: Yuhong Dai, Jiani Wang, Liwei Zhang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 3 : pp. 617–637
Abstract
Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research areas. While there have been many numerical algorithms for solving smooth convex-concave minimax problems, numerical algorithms for nonsmooth convex-concave minimax problems are rare. This 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 subproblem. This construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly chosen. We prove the global convergence of our algorithm under mild assumptions, without requiring strong convexity-concavity condition. Under the locally metrical subregularity of the solution mapping, we prove that our algorithm has the linear rate of convergence. Preliminary numerical results are reported to verify the efficiency of our algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2301-m2022-0099
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 3 : pp. 617–637
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Minimax optimization Convexity-concavity Global convergence Rate of convergence Locally metrical subregularity.
Author Details
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Optimality Conditions and Numerical Algorithms for a Class of Linearly Constrained Minimax Optimization Problems
Dai, Yu-Hong
Wang, Jiani
Zhang, Liwei
SIAM Journal on Optimization, Vol. 34 (2024), Iss. 3 P.2883
https://doi.org/10.1137/22M1535243 [Citations: 0]