Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 598632, 13 pages
doi:10.1155/2008/598632
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

Recommended by Jong Kim

Abstract

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.