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 \emph{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.

翻译：本文研究一类约束极小极大问题。具体而言，我们提出了一种用于求解该类问题的一阶增广拉格朗日方法，其子问题可简化为结构更为简单的极小极大问题，并通过作者在文[26]中近期发展的适当一阶方法进行求解。在适当假设下，我们为该一阶增广拉格朗日方法建立了以基本操作次数度量的\emph{运算复杂度}${\cal O}(\varepsilon^{-4}\log\varepsilon^{-1})$，以寻找约束极小极大问题的$\varepsilon$-KKT解。