A first-order augmented Lagrangian method for constrained minimax optimization

01/05/2023

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by   Zhaosong Lu, et al.

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In this paper we study a class of constrained minimax problems. In particular, we propose a first-order augmented Lagrangian method for solving them, whose subproblems turn out to be a much simpler structured minimax problem and are suitably solved by a first-order method recently developed in [26] by the authors. Under some suitable assumptions, an operation complexity of O(ε^-4logε^-1), measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an ε-KKT solution of the constrained minimax problems.