Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints

• URL: http://arxiv.org/abs/2212.04672v4
• Date: Sat, 27 Apr 2024 05:00:33 GMT
• Title: Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
• Authors: Huiling Zhang, Junlin Wang, Zi Xu, Yu-Hong Dai,
• Abstract summary: Non proximal minimax problems have attracted wide attention in machine learning, signal processing many other fields in recent years. We propose DAP algorithm for solving nonsmooth non-strongly concave minimax problems.
• Score: 4.70696854954921
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal-dual alternating proximal gradient (PDAPG) algorithm for solving nonsmooth nonconvex-(strongly) concave minimax problems with coupled linear constraints, respectively. The iteration complexity of the two algorithms are proved to be $\mathcal{O}\left( \varepsilon ^{-2} \right)$ (resp. $\mathcal{O}\left( \varepsilon ^{-4} \right)$) under nonconvex-strongly concave (resp. nonconvex-concave) setting to reach an $\varepsilon$-stationary point. To our knowledge, it is the first algorithm with iteration complexity guarantees for solving the nonconvex minimax problems with coupled linear constraints.

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