A generalized alternating direction method of multipliers with semi-proximal terms for convex composite conic programming

被引：23

作者：

Xiao Y. ^{[1
]}

Chen L. ^{[2
]}

Li D. ^{[3
]}

机构：

[1] Institute of Applied Mathematics, College of Mathematics and Statistics, Henan University, Kaifeng

[2] College of Mathematics and Econometrics, Hunan University, Changsha

[3] School of Mathematical Sciences, South China Normal University, Guangzhou

来源：

Mathematical Programming Computation | 2018年 / 10卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Alternating direction method of multipliers; Convex composite conic programming; Doubly non-negative semidefinite programming; Relaxation; Semi-proximal terms;

D O I：

10.1007/s12532-018-0134-9

中图分类号：

N94 [系统科学]; C94 [];

学科分类号：

0711 ; 081103 ; 1201 ;

摘要：

In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate accuracy. Our primary motivation is that this method, together with properly chosen semi-proximal terms, such as those generated by the recent advance of block symmetric Gauss–Seidel technique, is capable of tackling these problems. Moreover, the proposed method, which relaxes both the primal and the dual variables in a natural way with a common relaxation factor in the interval of (0, 2), has the potential of enhancing the performance of the classic ADMM. Extensive numerical experiments on various doubly non-negative semidefinite programming problems, with or without inequality constraints, are conducted. The corresponding results showed that all these multi-block problems can be successively solved, and the advantage of using the relaxation step is apparent. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature and The Mathematical Programming Society.

引用

页码：533 / 555

页数：22

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