Abstract and Applied Analysis

Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints

Lu-Chuan Ceng, Cheng-Wen Liao, Chin-Tzong Pang, and Ching-Feng Wen

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Abstract

We introduce and analyze a hybrid iterative algorithm by combining Korpelevich's extragradient method, the hybrid steepest-descent method, and the averaged mapping approach to the gradient-projection algorithm. It is proven that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of finitely many nonexpansive mappings, the solution set of a generalized mixed equilibrium problem (GMEP), the solution set of finitely many variational inclusions, and the solution set of a convex minimization problem (CMP), which is also a unique solution of a triple hierarchical variational inequality (THVI) in a real Hilbert space. In addition, we also consider the application of the proposed algorithm to solving a hierarchical variational inequality problem with constraints of the GMEP, the CMP, and finitely many variational inclusions.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 767109, 22 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412606014

Digital Object Identifier
doi:10.1155/2014/767109

Mathematical Reviews number (MathSciNet)
MR3230535

Zentralblatt MATH identifier
07023043

Citation

Ceng, Lu-Chuan; Liao, Cheng-Wen; Pang, Chin-Tzong; Wen, Ching-Feng. Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 767109, 22 pages. doi:10.1155/2014/767109. https://projecteuclid.org/euclid.aaa/1412606014


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