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arXiv · 2301.02060

A first-order augmented Lagrangian method for constrained minimax optimization

Zhaosong Lu·Sanyou Mei
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Abstract

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 developed in this paper. Under some suitable assumptions, an \emph{operation complexity} of $O(\varepsilon^{-4}\log\varepsilon^{-1})$, 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.

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Zhaosong Lu, Sanyou Mei. 2023-01-05. A first-order augmented Lagrangian method for constrained minimax optimization. https://arxiv.org/abs/2301.02060

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