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

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 (ϵ, √(ϵ))-second order stationary point(SSP) within 𝒪(ϵ^-1.5) iterations, which matches the best well known iteration complexity.