  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.
