A first-order method for nonconvex-strongly-concave constrained minimax optimization
arXiv:2512.22909v2 Announce Type: replace-cross
Abstract: 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 $O(varepsilon^{-3.5}logvarepsilon^{-1})$, measured in terms of its fundamental operations, for finding an $varepsilon$-KKT solution of the constrained minimax problem, which improves the previous best-known operation complexity by a factor of $varepsilon^{-0.5}$.
