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Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
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报告人:
Zi Xu, Professor, Shanghai University
邀请人:
Xin Liu, Professor
题目:
Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
时间地点:
10:00-11:00 March 24 (Friday), Z311
摘要:

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 and a primal dual proximal gradient (PDPG-L) algorithm for solving nonsmooth nonconvex-(strongly) concave and nonconvex-linear minimax problems with coupled linear constraints, respectively. The iteration complexity of the two algorithms are proved to be $O(\epsilon^{-2})$ (resp. $O(\epsilon^{-4})$) under nonconvex-strongly concave (resp. nonconvex-concave) setting and $O(\epsilon^{-3})$ under nonconvex-linear setting to reach an $\epsilon$-stationary point, respectively. To our knowledge, they are the first two algorithms with iteration complexity guarantee for solving the nonconvex minimax problems with coupled linear constraints.