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

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