Two trust region type algorithms for solving nonconvex-stronglyłinebreak 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) for solving nonconvex-strongly concave minimax problems. Both algorithms can find an mathcalOepsilon, sqrtepsilon-second-order stationary point (SSP) within mathcalOepsilon^-1.5 iterations, which matches the best well-known iteration complexity. Under mild assumptions, the MINIMAX-TRACE algorithm is proven to have local quadratic convergence.