题目：An Inexact Riemannian Proximal DC Algorithm for Nonsmooth Riemannian DC Optimization

时间：2025年3月21日，16:00—17:00

地点：数学楼2-2

讲座内容：Nonsmooth Riemannian optimization has gained significant attention recently, particularly for problems with sparse structures. While nonsmooth terms in these problems are often convex, regularization with nonsmooth difference-of-convex (DC) penalties typically offers superior statistical properties and recovery capabilities. In this talk, we introduce a new class of nonsmooth Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth DC function. We present application examples demonstrating the equivalence between our considered DC formulation and its corresponding $\ell_0$-regularized or $\ell_0$-constrained Riemannian optimization problem. To solve these problems, we propose an inexact Riemannian proximal algorithmic framework and show that it can return an $\epsilon$-Riemannian critical point within $\mathcal{O}(\epsilon^{-2})$ iterations and achieve an overall complexity of $\mathcal{O}(\epsilon^{-3})$. Numerical results on the sparse principal component analysis problem validate the effectiveness of the DC models and the proposed algorithms.

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”第七期第三层次培养对象。

邀请人：刘嘉 副教授