A proximal point algorithm revisit on the alternating direction method of multipliers

查看全文 作　　者：CAI [1]XingJu;GU [1]GuoYong;HE [1]BingSheng;YUAN [2]XiaoMing

机构地区：[1]Department of Mathematics, Nanjing University;[2]Department of Mathematics, Hong Kong Baptist University

出　　处：《Science China Mathematics》索引2013年第56卷第10期,共8页

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11001124 and 91130007);the Doctoral Fund of Ministry of Eduction of China(Grant No.20110091110004);the General Research Fund from Hong Kong Research Grants Council(Grant No.HKBU 203712) 摘　　要：The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an application of the proximal point algorithm(PPA)to the dual problem of the model under consideration.This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter.This primal illustration of ADMM is thus complemental to its dual illustration in the literature.This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily.A worst-case O(1/t)convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM. 关键词：交替方向法邻近点算法乘子法应用程序 PPA 线性约束目标函数对偶问题

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A proximal point algorithm revisit on the alternating direction method of multipliers

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