Taiwanese Journal of Mathematics

Hybrid Viscosity-like Approximation Methods for General Monotone Variational Inequalities

Lu-Chuan Ceng, Q. H. Ansari, and Juei-Ling Ho

Full-text: Open access

Abstract

In this paper, we introduce two implicit and explicit hybrid viscositylike approximation methods for solving a general monotone variational inequality, which covers their monotone variational inequality with $C = H$ as a special case. We use the contractions to regularize the general monotone variational inequality, where the monotone operators are the generalized complements of nonexpansive mappings and the solutions are sought in the set of fixed points of another nonexpansive mapping. Such general monotone variational inequality includes some monotone inclusions and some convex optimization problems to be solved over the fixed point sets of nonexpansive mappings. Both implicit and explicit hybrid viscosity-like approximation methods are shown to be strongly convergent. In the meantime, these results are applied to deriving the strong convergence theorems for a general monotone variational inequality with minimization constraint. An application in hierarchical minimization is also included.

Article information

Source
Taiwanese J. Math., Volume 15, Number 4 (2011), 1871-1896.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406385

Digital Object Identifier
doi:10.11650/twjm/1500406385

Mathematical Reviews number (MathSciNet)
MR2848995

Zentralblatt MATH identifier
1268.90097

Subjects
Primary: 90C25: Convex programming 47H05: Monotone operators and generalizations 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 65J15: Equations with nonlinear operators (do not use 65Hxx)

Keywords
hybrid viscosity-like approximation method general monotone variational inequality nonexpansive mapping projection minimization constraint

Citation

Ceng, Lu-Chuan; Ansari, Q. H.; Ho, Juei-Ling. Hybrid Viscosity-like Approximation Methods for General Monotone Variational Inequalities. Taiwanese J. Math. 15 (2011), no. 4, 1871--1896. doi:10.11650/twjm/1500406385. https://projecteuclid.org/euclid.twjm/1500406385


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