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

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arxiv 2402.09807 v1 pith:ZKJEPDWK submitted 2024-02-15 math.OC cs.LGstat.ML

Tongliang Yao , Zi Xu This is my paper · ORCID
classification math.OCcs.LGstat.ML
keywords minimaxalgorithmepsilonregiontrustalgorithmsconcavenonconvex-strongly
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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.

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  1. Gradient Norm Regularization Second-Order Algorithms for Solving Nonconvex-Strongly Concave Minimax Problems

    math.OC 2024-11 conditional novelty 6.0 of 10

    New trust-region and Levenberg-Marquardt algorithms for nonconvex-strongly concave minimax problems achieve the best known outer complexity and improve Hessian-vector product complexity to O(epsilon^-1.75).

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