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arXiv · 2402.09807

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

Tongliang Yao·Zi Xu
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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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Tongliang Yao, Zi Xu. 2024-02-15. Two trust region type algorithms for solving nonconvex-strongly concave minimax problems. https://arxiv.org/abs/2402.09807

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