Journal of Applied Mathematics
Volume 2011 (2011), Article ID 161853, 12 pages
http://dx.doi.org/10.1155/2011/161853
Research Article

The Levenberg-Marquardt-Type Methods for a Kind of Vertical Complementarity Problem

Shou-qiang Du1 and Yan Gao2

1College of Mathematics, Qingdao University, Qingdao 266071, China
2School of Management, University of Shanghai for Science and Technology, Shanghai 200093, China

Received 30 August 2011; Accepted 12 October 2011

Academic Editor: Chong Lin

Copyright © 2011 Shou-qiang Du and Yan Gao. 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

Two kinds of the Levenberg-Marquardt-type methods for the solution of vertical complementarity problem are introduced. The methods are based on a nonsmooth equation reformulation of the vertical complementarity problem for its solution. Local and global convergence results and some remarks about the two kinds of the Levenberg-Marquardt-type methods are also given. Finally, numerical experiments are reported.