Journal of Applied Mathematics
Volume 2012 (2012), Article ID 215160, 15 pages
http://dx.doi.org/10.1155/2012/215160
Research Article

A Decomposition Algorithm for Convex Nondifferentiable Minimization with Errors

Yuan Lu,1 Li-Ping Pang,2 Jie Shen,3 and Xi-Jun Liang2

1School of Sciences, Shenyang University, Shenyang 110044, China
2School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
3School of Mathematics, Liaoning Normal University, Dalian 116029, China

Received 29 July 2011; Accepted 25 October 2011

Academic Editor: Chein-Shan Liu

Copyright © 2012 Yuan Lu 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

A decomposition algorithm based on proximal bundle-type method with inexact data is presented for minimizing an unconstrained nonsmooth convex function . At each iteration, only the approximate evaluation of and its approximate subgradients are required which make the algorithm easier to implement. It is shown that every cluster of the sequence of iterates generated by the proposed algorithm is an exact solution of the unconstrained minimization problem. Numerical tests emphasize the theoretical findings.