Journal of Applied Mathematics
Volume 2013 (2013), Article ID 714397, 8 pages
Research Article

New Double Projection Algorithm for Solving Variational Inequalities

Department of Mathematics and Computer Science, Yangtze Normal University, Fuling, Chongqing 408100, China

Received 7 January 2013; Accepted 20 May 2013

Academic Editor: Zhongxiao Jia

Copyright © 2013 Lian Zheng. 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.


We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments prove that our algorithms are efficient.