Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 401835, 17 pages
Research Article

A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem

1School of Mathematics and Information Science, Weifang University, Weifang, Shandong 261061, China
2College of Applied Science, Beijing University of Technology, Beijing 100022, China

Received 22 November 2011; Accepted 29 January 2012

Academic Editor: Mohammad Younis

Copyright © 2012 Meixia Li and Haitao Che. 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.


Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic) convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.