Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 15, Number 4 (2011), 1871-1896.
Hybrid Viscosity-like Approximation Methods for General Monotone Variational Inequalities
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.
Taiwanese J. Math., Volume 15, Number 4 (2011), 1871-1896.
First available in Project Euclid: 18 July 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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)
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