Convex Relaxation Algorithm for a Structured Simultaneous Low-Rank and Sparse Recovery Problem

作     者：Le Han Xiao-Lan Liu 

作者机构：Department of MathematicsSouth China University of TechnologyGuangzhou 510641China 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2015年第3卷第3期

页      面：363-379页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work is supported by the National Natural Science Foundation of China(Nos.61402182 and 61273295) 

主　　题：Simultaneous low-rank and sparse recovery Convex relaxation Error bound 

摘      要：This paper is concerned with the structured simultaneous low-rank and sparse recovery,which can be formulated as the rank and zero-norm regularized least squares problem with a hard constraint diag(■)=*** this class of NP-hard problems,we propose a convex relaxation algorithm by applying the accelerated proximal gradient method to a convex relaxation model,which is yielded by the smoothed nuclear norm and the weighted l1-norm regularized least squares problem.A theoretical guarantee is provided by establishing the error bounds of the iterates to the true solution under mild restricted strong convexity *** the best of our knowledge,this work is the first one to characterize the error bound of the iterates of the algorithm to the true ***,numerical results are reported for some random test problems and synthetic data in subspace clustering to verify the efficiency of the proposed convex relaxation algorithm.