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