Computational Optimization and Applications
, Volume 1, Issue 1, pp 93111
First online:
Application of the alternating direction method of multipliers to separable convex programming problems
 Masao FukushimaAffiliated withDepartment of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University
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This paper presents a decomposition algorithm for solving convex programming problems with separable structure. The algorithm is obtained through application of the alternating direction method of multipliers to the dual of the convex programming problem to be solved. In particular, the algorithm reduces to the ordinary method of multipliers when the problem is regarded as nonseparable. Under the assumption that both primal and dual problems have at least one solution and the solution set of the primal problem is bounded, global convergence of the algorithm is established.
Keywords
Convex programming separable problems decomposition alternating direction method of multipliers parallel algorithm Title
 Application of the alternating direction method of multipliers to separable convex programming problems
 Journal

Computational Optimization and Applications
Volume 1, Issue 1 , pp 93111
 Cover Date
 199210
 DOI
 10.1007/BF00247655
 Print ISSN
 09266003
 Online ISSN
 15732894
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Convex programming
 separable problems
 decomposition
 alternating direction method of multipliers
 parallel algorithm
 Industry Sectors
 Authors

 Masao Fukushima ^{(1)}
 Author Affiliations

 1. Department of Applied Mathematics and Physics, Faculty of Engineering, Kyoto University, 606, Kyoto, Japan