Two trust region type algorithms for solving nonconvex-strongly concave minimax problems

Abstract

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.