数学科学学院学术报告[2024] 141号

(高水平大学建设系列报告1021号)

报告题目: RADA: A Flexible Algorithmic Framework for Nonconvex-Linear Minimax Problems on Riemannian Manifolds

报告人：姜波 教授（南京师范大学）

报告时间：2024年12月25日上午10:30-11:30

讲座地点：深圳大学粤海校区汇星楼一号教室

报告内容：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 (RADA) 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 connections 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. This is a joint work with Meng Xu, Ya-Feng Liu, and Anthony Man-Cho So.

报告人简介：姜波，南京师范大学数学科学学院教授，博士生导师。2008 年本科毕业于中国石油大学 (华东)，2013 年博士毕业于中国科学院数学与系统科学研究院，2014 年 8 月入职南京师范大学。主要研究方向为流形约束优化算法与理论，在 Math. Program., SIAM J. Optim, SIAM J. Sci. Comput., IEEE 汇刊等期刊和NeurIPS上发表多篇学术论文。曾入选第三届中国科协青年人才托举工程项目，获得2022年中国运筹学会青年科技奖，并于2024年入选江苏省“333工程”第三层次培养对象。

欢迎师生参加！

邀请人：胡耀华

　　　　　　　　　　　　　　　　　　　　　　 数学科学学院

　　　　　　　　　　　　　　　　　　　　 2024年12月23日