报告题目：Smoothing algorithms for nonsmooth optimization over the Stiefel manifold with applications to the graph Fourier basis problem

报告人：李洽副教授，中山大学

报告时间：2024年10月25日（周五）14:00-15:00

报告地点：腾讯会议ID：400-737-414

摘要：In this talk, we consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a nonsmooth Lipschitz continuous convex function composed with a linear mapping. Besides, we are interested in its application to the graph Fourier basis problem. We propose three numerical algorithms for solving this problem, by combining smoothing methods and some existing algorithms for smooth optimization over the Stiefel manifold. In particular, we approximate the aforementioned nonsmooth convex function by its Moreau envelope in our smoothing methods, and prove that the Moreau envelope has many favorable properties. Thanks to this and the scheme for updating the smoothing parameter, we show that any accumulation point of the solution sequence generated by the proposed algorithms is a stationary point of the original optimization problem. Numerical experiments on building graph Fourier basis are conducted to demonstrate the efficiency of the proposed algorithms. 

报告人简介：李洽，中山大学计算机学院副教授，博士生导师，现任中山大学计算机学院数据科学系副主任，广东省计算数学学会常务理事兼副秘书长，广东省计算科学重点实验室成员。2013年获中山大学数学（信息计算科学方向）博士学位，博士期间曾赴美国Syracuse University数学系访问一年。研究方向包括最优化理论与算法及在机器学习、大数据分析、图像处理等领域中的应用，研究成果发表于SIAM Journal on Optimization, Applied and Computational Harmonic Analysis, Inverse Problems等期刊。主持国家级科研项目四项（包括国基面上两项、国基青年与国防类一项），参与项目包括国基重大研究计划集成项目、科技部重大专项等。

邀请人：向道红