Three-step relaxed hybrid steepest-descent methods for variational inequalities

doi:10.1007/s10483-007-0805-x

Applied Mathematics and Mechanics (English Edition) ›› 2007, Vol. 28 ›› Issue (8): 1029-1036 .doi: https://doi.org/10.1007/s10483-007-0805-x

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Three-step relaxed hybrid steepest-descent methods for variational inequalities

DING Xie-ping, LIN Yen-cherng, YAO Jen-chih

1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China;
2. General Education Center, China Medical University, Taichung 404, Taiwan, P. R. China;
3. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, P. R. China

Received:2006-11-19 Revised:2007-06-25 Online:2007-08-18 Published:2007-08-18
Contact: DING Xie-ping

Abstract

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

Key words: Hilbert space, variational inequalities, relaxed hybrid steepest-descent method, strong convergence, nonexpansive mapping

2010 MSC Number:

DING Xie-ping;LIN Yen-cherng;YAO Jen-chih. Three-step relaxed hybrid steepest-descent methods for variational inequalities. Applied Mathematics and Mechanics (English Edition), 2007, 28(8): 1029-1036 .

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Three-step relaxed hybrid steepest-descent methods for variational inequalities

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