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

arXiv:2212.04672v3 Announce Type: replace-cross
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 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 $\mathcal{O}\left( \varepsilon ^{-2} \right)$ (resp. $\mathcal{O}\left( \varepsilon ^{-4} \right)$) under nonconvex-strongly concave …

abstract algorithm algorithms arxiv attention constraints cs.lg fields gradient linear machine machine learning math.oc minimax paper primal processing signal stat.ml type