Convergence Analysis of the Generalized Alternating Direction Method of Multipliers with Logarithmic-Quadratic Proximal Regularization

被引：5

作者：

Li, Min ^{[1
]}

Li, Xinxin ^{[2
]}

Yuan, Xiaoming ^{[2
]}

机构：

[1] Southeast Univ, Sch Econ & Management, Nanjing 210096, Jiangsu, Peoples R China

[2] Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2015年 / 164卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Generalized alternating direction method of multipliers; Logarithmic-quadratic proximal method; Convergence rate; Variational inequality; DECOMPOSITION METHODS; POINT ALGORITHM;

D O I：

10.1007/s10957-014-0567-x

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We consider combining the generalized alternating direction method of multipliers, proposed by Eckstein and Bertsekas, with the logarithmic-quadratic proximal method proposed by Auslender, Teboulle, and Ben-Tiba for solving a variational inequality with separable structures. For the derived algorithm, we prove its global convergence and establish its worst-case convergence rate measured by the iteration complexity in both the ergodic and nonergodic senses.

引用

页码：218 / 233

页数：16

共 30 条

[11]

Gabay D., 1976, Computers & Mathematics with Applications, V2, P17, DOI 10.1016/0898-1221(76)90003-1

[12]

GLOWINSKI R, 1975, REV FR AUTOMAT INFOR, V9, P41

[13]

GLOWINSKI R., 1984, Numerical Methods for Nonlinear Variational Problems

[14]

GOLSHTEIN EG, 1979, MATH PROGRAM STUD, V10, P86, DOI 10.1007/BFb0120845

[15]

He B.S., 2013, NONERGODIC CONVERGEN

[16] ON THE O(1/n) CONVERGENCE RATE OF THE DOUGLAS-RACHFORD ALTERNATING DIRECTION METHOD [J].

He, Bingsheng ;

Yuan, Xiaoming .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2012, 50 (02) :700-709

[17]

He BS, 2006, J COMPUT MATH, V24, P33

[18] A new inexact alternating directions method for monotone variational inequalities [J].

He, BS ;

Liao, LZ ;

Han, DR ;

Yang, H .

MATHEMATICAL PROGRAMMING, 2002, 92 (01) :103-118

[19] A variable-penalty alternating directions method for convex optimization [J].

Kontogiorgis, S ;

Meyer, RR .

MATHEMATICAL PROGRAMMING, 1998, 83 (01) :29-53

[20]

MARTINET B, 1970, REV FR AUTOMAT INFOR, V4, P154

← 1 2 3 →