Two trust region type algorithms for solving nonconvex-strongly concave minimax problems
<|reference_start|>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 $(\epsilon, \sqrt{\epsilon})$-second order stationary point(SSP) within $\mathcal{O}(\epsilon^{-1.5})$ iterations, which matches the best well known iteration complexity.<|reference_end|>
@article{yao2024two,
    title={Two trust region type algorithms for solving nonconvex-strongly concave
  minimax problems},
    author={Tongliang Yao and Zi Xu},
    journal={arXiv preprint arXiv:2402.09807},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.09807},
    primaryClass={math.OC cs.LG stat.ML}
}