DIFFERENCE-OF-CONVEX ALGORITHMS FOR A CLASS OF SPARSE GROUP l0 REGULARIZED OPTIMIZATION PROBLEMS

作     者：Li, Wenjing Bian, Wei Toh, Kim-Chuan 

作者机构：Natl Univ Singapore Dept Math 10 Lower Kent Ridge Rd Singapore Singapore Harbin Inst Technol Sch Math Harbin 150001 Peoples R China Natl Univ Singapore Inst Operat Res & Analyt 10 Lower Kent Ridge Rd Singapore Singapore 

出 版 物：《SIAM JOURNAL ON OPTIMIZATION》 

年 卷 期：2022年第32卷第3期

页      面：1614-1641页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：China Scholarship Council National Natural Science Foundation of China [11871178, 62176073] Ministry of Education, Singapore [MOE-2019-T3-1-010] 

主　　题：sparse group l(0) regularization continuous relaxation DC algorithm global convergence 

摘      要：In this paper, we consider a class of sparse group l(0) 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 l(0) 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 l(0) 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.