12月17日午餐会参与情况统计

摘要：In this talk, we focus on a class of nonconvex-linear minimax problems on Riemannian manifolds, which are equivalent to Riemannian nonsmooth composite problems and have wide applications in machine learning and signal processing. To solve this class of problems, we propose a flexible Riemannian alternating descent ascent (RADA) algorithmic framework and establish that it achieves the best-known iteration complexity to date. Various customized, simple, yet efficient algorithms can be incorporated within this framework to address different problem scenarios. We also highlight intriguing similarities and differences between algorithms developed under our framework and existing methods, providing insights into why the former outperform the latter. Finally, we present numerical results on sparse principal component analysis (PCA), fair PCA, and sparse spectral clustering, demonstrating the superior performance of the proposed algorithms.

报告人简介：徐勐，中国科学院数学与系统科学研究院博士生，导师为刘亚锋教授。研究方向为最优化方法和应用，尤其是流形约束的非光滑优化和极小极大优化，及其在信号处理和机器学习中的应用。曾获2024年中国科学院数学与系统科学研究院华罗庚奖学金。