A first-order method for nonconvex-strongly-concave constrained minimax optimization

In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax problems and suitably solved by a first-order method developed in this paper that leverages the strong concavity structure. Under suitable assumptions, the proposed method achieves an operation complexity of (Formula presented.), measured in terms of its fundamental operations, for finding an ε-KKT solution of the constrained minimax problem, which improves the previous best-known operation complexity by a factor of (Formula presented.).