Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 598632, 13 pages
Research Article

Finite-Step Relaxed Hybrid Steepest-Descent Methods for Variational Inequalities

Yen-Cherng Lin

Department of Occupational Safety and Health, General Education Center, China Medical University, Taichung 404, Taiwan

Received 22 August 2007; Revised 2 January 2008; Accepted 13 March 2008

Academic Editor: Jong Kim

Copyright © 2008 Yen-Cherng Lin. 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.


The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space was studied. A new finite-step relaxed hybrid steepest-descent method for this class of variational inequalities was introduced. Strong convergence of this method was established under suitable assumptions imposed on the algorithm parameters.