## Abstract and Applied Analysis

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

### 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

#### 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