Table of Contents
ISRN Mathematical Analysis
Volume 2013 (2013), Article ID 727892, 8 pages
http://dx.doi.org/10.1155/2013/727892
Research Article

An Improved Two-Step Method for Generalized Variational Inequalities

School of Management Science, Qufu Normal University, Rizhao, Shandong 276800, China

Received 22 July 2013; Accepted 30 August 2013

Academic Editors: R. D. Chen and Y. Dai

Copyright © 2013 Haibin Chen. 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 propose an improved two-step extragradient algorithm for pseudomonotone generalized variational inequalities. It requires two projections at each iteration and allows one to take different stepsize rules. Moreover, from a geometric point of view, it is shown that the new method has a long stepsize, and it guarantees that the distance from the next iterative point to the solution set has a large decrease. Under mild conditions, we show that the method is globally convergent, and then the -linearly convergent property of the method is proven if a projection-type error bound holds locally.