Journal of the Operations Research Society of China ›› 2026, Vol. 14 ›› Issue (2): 502-520.doi: 10.1007/s40305-024-00550-3

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  • 收稿日期:2024-04-25 修回日期:2024-05-13 出版日期:2026-06-30 发布日期:2026-07-06
  • 通讯作者: Zi Xu E-mail:xuzi@shu.edu.cn
  • 作者简介:Hui-Ling Zhang,E-mail:zhanghl1209@shu.edu.cn

An Alternating Proximal Gradient Algorithm for Nonsmooth Nonconvex-Linear Minimax Problems with Coupled Linear Constraints

Hui-Ling Zhang1, Zi Xu1,2   

  1. 1 Department of Mathematics, Shanghai University, Shanghai 200444, China;
    2 Newtouch Center for Mathematics of Shanghai University, Shanghai University, Shanghai 200444, China
  • Received:2024-04-25 Revised:2024-05-13 Online:2026-06-30 Published:2026-07-06
  • Contact: Zi Xu E-mail:xuzi@shu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (No. 12071279).

Abstract: In this paper, we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints, which have attracted wide attention in machine learning, signal processing and many other fields in recent years. The iteration complexity of the proposed algorithm is proved to be $\mathcal{O}\left(\varepsilon^{-3}\right)$ to reach an $\varepsilon$-stationary point. To our knowledge, this is the first algorithm with iteration complexity guarantee for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints.

Key words: Minimax optimization problem, Alternating proximal gradient algorithm, Iteration complexity, Machine learning

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