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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 139609, 14 pages
http://dx.doi.org/10.1155/2012/139609
Research Article

New Nonsmooth Equations-Based Algorithms for -Norm Minimization and Applications

Lei Wu1 and Zhe Sun2

1College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
2College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China

Received 18 September 2012; Revised 8 December 2012; Accepted 9 December 2012

Academic Editor: Changbum Chun

Copyright © 2012 Lei Wu and Zhe Sun. 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

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the -norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving -norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms.