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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 697474, 7 pages
http://dx.doi.org/10.1155/2013/697474
Research Article

An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization

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

Received 22 January 2013; Revised 31 March 2013; Accepted 1 April 2013

Academic Editor: Gue Lee

Copyright © 2013 Jie Shen 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

An implementable algorithm for solving a nonsmooth convex optimization problem is proposed by combining Moreau-Yosida regularization and bundle and quasi-Newton ideas. In contrast with quasi-Newton bundle methods of Mifflin et al. (1998), we only assume that the values of the objective function and its subgradients are evaluated approximately, which makes the method easier to implement. Under some reasonable assumptions, the proposed method is shown to have a Q-superlinear rate of convergence.