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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 680768, 8 pages
http://dx.doi.org/10.1155/2013/680768
Research Article

Convergence Analysis of Alternating Direction Method of Multipliers for a Class of Separable Convex Programming

1School of Mathematical Science and Key Laboratory for NSLSCS of Jiangsu Province, Nanjing Normal University, Nanjing, Jiangsu 210023, China
2College of Mathematics and Information, China West Normal University, Nanchong, Sichuan 637009, China

Received 19 July 2013; Accepted 30 July 2013

Academic Editor: Xu Minghua

Copyright © 2013 Zehui Jia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The purpose of this paper is extending the convergence analysis of Han and Yuan (2012) for alternating direction method of multipliers (ADMM) from the strongly convex to a more general case. Under the assumption that the individual functions are composites of strongly convex functions and linear functions, we prove that the classical ADMM for separable convex programming with two blocks can be extended to the case with more than three blocks. The problems, although still very special, arise naturally from some important applications, for example, route-based traffic assignment problems.