Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems
Joint Authors
Pang, Chin-Tzong
Ceng, Lu-Chuan
Wen, Ching-Feng
Liao, Cheng-Wen
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-26
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
We introduce and analyze a hybrid iterative algorithm by virtue of Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, and 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 infinitely many nonexpansive mappings, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inequality problems (VIPs), the solution set of general system of variational inequalities (GSVI), and the set of minimizers of convex minimization problem (CMP), which is just 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 solve a hierarchical fixed point problem with constraints of finitely many GMEPs, finitely many VIPs, GSVI, and CMP.
The results obtained in this paper improve and extend the corresponding results announced by many others.
American Psychological Association (APA)
Ceng, Lu-Chuan& Liao, Cheng-Wen& Pang, Chin-Tzong& Wen, Ching-Feng. 2014. Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-25.
https://search.emarefa.net/detail/BIM-447986
Modern Language Association (MLA)
Ceng, Lu-Chuan…[et al.]. Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems. Journal of Applied Mathematics No. 2014 (2014), pp.1-25.
https://search.emarefa.net/detail/BIM-447986
American Medical Association (AMA)
Ceng, Lu-Chuan& Liao, Cheng-Wen& Pang, Chin-Tzong& Wen, Ching-Feng. Triple Hierarchical Variational Inequalities with Constraints of Mixed Equilibria, Variational Inequalities, Convex Minimization, and Hierarchical Fixed Point Problems. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-25.
https://search.emarefa.net/detail/BIM-447986
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447986