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