深圳大学数学科学学院

荔园学者Colloquium第一百一十七期

讲座题目: Difference-of-Convex Algorithms for a Class of Sparse Group ℓ0 Regularized Optimization Problems

主讲人：边伟 教授（哈尔滨工业大学）

讲座时间：2025年3月1日上午10：30-11：00

讲座地点：深圳大学粤海校区汇星楼四号教室

内容摘要：In this paper, we consider a class of sparse group ℓ0 regularized optimization problems. First, we give a continuous relaxation model of the considered problem and define a class of stationary points of the relaxation problem. Then, we establish the equivalence of these two problems in the sense of global minimizers, and prove that the defined stationary point is equivalent to the local minimizer of the considered sparse group ℓ0 regularized problem with a desirable bound from its global minimizers. Further, based on the difference-of-convex (DC) structure of the relaxation problem, we design two DC algorithms to solve the relaxation problem. We prove that any accumulation point of the iterates generated by them is a local minimizer with a desirable bound for the considered sparse group ℓ0 problem. In particular, all accumulation points have a common support set and their zero entries can be attained within finite iterations. Moreover, we give the global convergence analysis of the proposed algorithms. Finally, we perform some numerical experiments to show the efficiency of the proposed algorithms.

主讲人简介：边伟，哈尔滨工业大学数学学院，教授、博士生导师。2004年和2009年于哈尔滨工业大学分别获得学士和博士学位。2010-2012年访问香港理工大学，跟随陈小君教授从事博士后工作。主要研究领域为：最优化理论与算法。先后在 Math. Program., Math. Oper. Res., SIAM J. Optim., SIAM J. Numer. Anal., SIAM J. Sci. Comput., SIAM J. Imaging Sci. 等期刊发表多篇学术论文。先后获国家级青年人才称号和国家杰出青年基金项目。现任SCI期刊Journal of Optimization Theory and Application编委，中国运筹学会常务理事，黑龙江省数学会常务理事，中国运筹学会数学规划分会理事等。

欢迎师生参加！

邀请人：数学科学学院（胡耀华）

　 数学科学学院

2025年2月28日