报告题目 (Title)：A Flexible Algorithmic Framework for Nonconvex-Linear Minimax Problems on Riemannian Manifolds (黎曼流形上的非凸线性极小极大问题的一种灵活的算法框架)

报告人 (Speaker)：刘亚锋（中国科学院数学与系统科学研究院，国际知名专家）

报告时间 (Time)：2024年 12月6日 (周五) 14:00-18:00

报告地点 (Place)：校本部GJ303

邀请人(Inviter)：徐姿 教授

主办部门：理学院数学系

报告摘要：

Recently, there has been growing interest in minimax problems on Riemannian manifolds due to their wide applications in machine learning and signal processing. Although many algorithms have been developed for minimax problems in the Euclidean setting, relatively few works studied minimax problems on manifolds. In this talk, we focus on the nonconvex-linear minimax problem on Riemannian manifolds. We propose a flexible Riemannian alternating descent ascent algorithmic framework and prove that it achieves the best-known iteration complexity known to date. Various customized simple yet efficient algorithms can be incorporated within the proposed algorithmic framework and applied to different problem scenarios. We also reveal intriguing similarities and differences between the algorithms developed within our proposed framework and existing algorithms, which provide important insights into why the former outperform the latter. Lastly, we report extensive numerical results on sparse principal component analysis (PCA), fair PCA, and sparse spectral clustering to demonstrate the superior performance of the proposed algorithms.