An efficient partial parallel method with scaling step size strategy for three-block convex optimization problems

作     者：Jiang, Yaning Han, Deren Cai, Xingju 

作者机构：Nanjing Univ Dept Math Nanjing 210093 Peoples R China Beihang Univ Sch Math Sci LMIB Beijing 100191 Peoples R China Nanjing Normal Univ Sch Math Sci Jiangsu Key Lab NSLSCS Nanjing 210093 Peoples R China 

出 版 物：《MATHEMATICAL METHODS OF OPERATIONS RESEARCH》 (运筹学研究中的数学方法)

年 卷 期：2022年第96卷第3期

页      面：383-419页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0701[理学-数学] 

基　　金：NSFC [11625105  12131004  11871279  11571178] 

主　　题：Convex programming Alternating direction method of multipliers Partially parallel splitting method Convergence rate 

摘      要：A popular optimization model arising from image processing is the separable optimization problem whose objective function is the sum of three independent functions, and the variables are coupled by a linear equality. In this paper, we propose to solve such problem by a new partially parallel splitting method, whose step sizes for the primal and the dual variables in correction step are not necessarily identical. We establish the global convergence, and study the convergence rate on this varying ADMM-based prediction-correction method named as VAPCM. We derive the worst-case O(1/t) convergence rate in both the ergodic and non-ergodic senses. We also show that the convergence rate can be improved to o(1/t). Moreover, under the error bound assumptions, we establish the global linear convergence of VAPCM. We apply the new method to solve problems in robust principal component analysis and image decomposition. Numerical results indicate that the new method is efficient.