Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 349178, 20 pages
http://dx.doi.org/10.1155/2012/349178
Research Article

A Filter Algorithm with Inexact Line Search

Meiling Liu,1 Xueqian Li,2 and Qinmin Wu3

1Department of Mathematics, Tongji University, Shanghai 200092, China
2Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
3School of Management, Fudan University, Shanghai 200433, China

Received 25 October 2011; Accepted 18 December 2011

Academic Editor: Dongdong Ge

Copyright © 2012 Meiling Liu 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 filter algorithm with inexact line search is proposed for solving nonlinear programming problems. The filter is constructed by employing the norm of the gradient of the Lagrangian function to the infeasibility measure. Transition to superlinear local convergence is showed for the proposed filter algorithm without second-order correction. Under mild conditions, the global convergence can also be derived. Numerical experiments show the efficiency of the algorithm.