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

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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