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：带约束极小极大优化问题的一阶增广Lagrange方法
翻译后的摘要：
本文研究了一类带约束的极小极大问题。具体而言，我们提出了一种一阶增广Lagrange方法来解决这类问题，其中子问题变得更加简单，其结构是最近由作者在文献[26]中开发的一种一阶方法适当地解决。在一些适当的假设下，该方法可以找到带约束的极小极大问题的$\varepsilon$-KKT解，其操作复杂度为$ {\cal O}(\varepsilon^{-4}\log\varepsilon^{-1}) $ 。
相关内容
微信扫码咨询专知VIP会员