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Advances in Operations Research
Volume 2012, Article ID 281396, 20 pages
Research Article

An Asymmetric Proximal Decomposition Method for Convex Programming with Linearly Coupling Constraints

1Institute of System Engineering, Southeast University, Nanjing 210096, China
2Department of Mathematics, Nanjing University, Nanjing 210093, China
3Department of Mathematics, Guangxi Normal University, Guilin 541004, China

Received 17 November 2011; Accepted 10 January 2012

Academic Editor: Abdellah Bnouhachem

Copyright © 2012 Xiaoling Fu 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.


The problems studied are the separable variational inequalities with linearly coupling constraints. Some existing decomposition methods are very problem specific, and the computation load is quite costly. Combining the ideas of proximal point algorithm (PPA) and augmented Lagrangian method (ALM), we propose an asymmetric proximal decomposition method (AsPDM) to solve a wide variety separable problems. By adding an auxiliary quadratic term to the general Lagrangian function, our method can take advantage of the separable feature. We also present an inexact version of AsPDM to reduce the computation load of each iteration. In the computation process, the inexact version only uses the function values. Moreover, the inexact criterion and the step size can be implemented in parallel. The convergence of the proposed method is proved, and numerical experiments are employed to show the advantage of AsPDM.