Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 765206, 11 pages
doi:10.1155/2010/765206
Research Article

Regularization and Iterative Methods for Monotone Variational Inequalities

Xiubin Xu1 and Hong-Kun Xu2

1Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
2Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan

Received 16 September 2009; Accepted 23 November 2009

Academic Editor: Mohamed A. Khamsi

Copyright © 2010 Xiubin Xu and Hong-Kun Xu. 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

We provide a general regularization method for monotone variational inequalities, where the regularizer is a Lipschitz continuous and strongly monotone operator. We also introduce an iterative method as discretization of the regularization method. We prove that both regularization and iterative methods converge in norm.