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Journal of Applied Mathematics
Volume 2014, Article ID 540450, 8 pages
http://dx.doi.org/10.1155/2014/540450
Research Article

A Line-Search-Based Partial Proximal Alternating Directions Method for Separable Convex Optimization

1College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
2Department of Mathematics, Hunan First Normal University, Changsha 410205, China
3College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China

Received 26 January 2014; Accepted 25 April 2014; Published 7 May 2014

Academic Editor: Jose L. Gracia

Copyright © 2014 Yu-hua Zeng 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

We propose an appealing line-search-based partial proximal alternating directions (LSPPAD) method for solving a class of separable convex optimization problems. These problems under consideration are common in practice. The proposed method solves two subproblems at each iteration: one is solved by a proximal point method, while the proximal term is absent from the other. Both subproblems admit inexact solutions. A line search technique is used to guarantee the convergence. The convergence of the LSPPAD method is established under some suitable conditions. The advantage of the proposed method is that it provides the tractability of the subproblem in which the proximal term is absent. Numerical tests show that the LSPPAD method has better performance compared with the existing alternating projection based prediction-correction (APBPC) method if both are employed to solve the described problem.