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.
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页码：218 / 233
页数：16
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