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

Joint Authors

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

Source

Abstract and Applied Analysis

Issue

Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-22, 22 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2014-07-03

Country of Publication

Egypt

No. of Pages

22

Main Subjects

Mathematics

Abstract EN

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.

American Psychological Association (APA)

Ceng, Lu-Chuan& Liao, Cheng-Wen& Pang, Chin-Tzong& Wen, Ching-Feng. 2014. Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-22.
https://search.emarefa.net/detail/BIM-1014751

Modern Language Association (MLA)

Ceng, Lu-Chuan…[et al.]. Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints. Abstract and Applied Analysis No. 2014 (2014), pp.1-22.
https://search.emarefa.net/detail/BIM-1014751

American Medical Association (AMA)

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. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-22.
https://search.emarefa.net/detail/BIM-1014751

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1014751