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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 \({\cal O}(\varepsilon^{-4}\log\varepsilon^{-1})\), measured by its fundamental operations, is established for the first-order augmented Lagrangian method for finding an \(\varepsilon\)-KKT solution of the constrained minimax problems.
Citation
arXiv preprint arXiv:2301.02060, 2023
Article
View A first-order augmented Lagrangian method for constrained minimax optimization