A note on augmented Lagrangian-based parallel splitting method

作     者：Wang, Kai Desai, Jitamitra He, Hongjin 

作者机构：Nanyang Technol Univ Sch Mech & Aerosp Engn Singapore 639798 Singapore Hangzhou Dianzi Univ Sch Sci Dept Math Hangzhou 310018 Zhejiang Peoples R China 

出 版 物：《OPTIMIZATION LETTERS》 (最优化通信)

年 卷 期：2015年第9卷第6期

页      面：1199-1212页

核心收录：

学科分类：0810[工学-信息与通信工程] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070104[理学-应用数学] 081001[工学-通信与信息系统] 0701[理学-数学] 

基　　金：NSFC Zhejiang Provincial NSFC [LZ14A010003] MOE (Singapore) [M4011083] 

主　　题：Augmented Lagrangian method Jacobian decomposition Convex minimization Strongly convex function 

摘      要：We consider the linearly constrained separable convex minimization problem, whose objective function consists of the sum of individual convex functions in the absence of any coupling variables. While augmented Lagrangian-based decomposition methods have been well developed in the literature for solving such problems, a noteworthy requirement of these methods is that an additional correction step is a must to guarantee their convergence. This note shows that a straightforward Jacobian decomposition of the augmented Lagrangian method is globally convergent if the involved functions are further assumed to be strongly convex.