In this paper, we propose a Minimax Trust Region (MINIMAX-TR) algorithm and a Minimax Trust Region Algorithm with Contractions and Expansions(MINIMAX-TRACE) algorithm for solving nonconvex-strongly concave minimax problems. Both algorithms can find an $(\epsilon, \sqrt{\epsilon})$-second order stationary point(SSP) within $\mathcal{O}(\epsilon^{-1.5})$ iterations, which matches the best well known iteration complexity.

翻译：本文提出了一种极小极大信赖域（MINIMAX-TR）算法和一种带收缩与扩张的极小极大信赖域（MINIMAX-TRACE）算法，用于求解非凸-强凹极小极大问题。两种算法均能在$\mathcal{O}(\epsilon^{-1.5})$次迭代内找到$(\epsilon, \sqrt{\epsilon})$-二阶平稳点（SSP），这与已知的最佳迭代复杂度相匹配。