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Three-step relaxed hybrid steepest-descent methods for variational inequalities |
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| Authors: | Ding Xie-ping Lin Yen-cherng Yao Jen-chih |
| Affiliation: | College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, P. R. China;General Education Center, China Medical University, Taichung 404, Taiwan, P. R. China;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, P. R. China |
| 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. |
| Keywords: | variational inequalities relaxed hybrid steepest-descent method strong convergence nonexpansive mapping Hilbert space |
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