Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
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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 corresponding iteration complexity of the two algorithms are proved to be 𝒪( ε ^-2) and 𝒪( ε ^-3) to reach an ε-stationary point, respectively. To our knowledge, they are the first two algorithms with iteration complexity guarantee for solving the two classes of minimax problems.
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