Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities
We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove that, under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of i...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/980352 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832552423654162432 |
|---|---|
| author | L. C. Ceng A. Latif C. F. Wen A. E. Al-Mazrooei |
| author_facet | L. C. Ceng A. Latif C. F. Wen A. E. Al-Mazrooei |
| author_sort | L. C. Ceng |
| collection | DOAJ |
| description | We introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove 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 inclusions, and the solution set of general system of variational inequalities (GSVI), 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 for solving a hierarchical variational inequality problem with constraints of finitely many GMEPs, finitely many variational inclusions, and the GSVI. The results obtained in this paper improve and extend the corresponding results announced by many others. |
| format | Article |
| id | doaj-art-4336ec4ddab04f30862fb96a2e4c3455 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-4336ec4ddab04f30862fb96a2e4c34552025-02-03T05:58:37ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/980352980352Hybrid Steepest-Descent Methods for Triple Hierarchical Variational InequalitiesL. C. Ceng0A. Latif1C. F. Wen2A. E. Al-Mazrooei3Department of Mathematics, Shanghai Normal University, and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanDepartment of Mathematics, College of Science, University of Jeddah, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe introduce and analyze a relaxed iterative algorithm by combining Korpelevich’s extragradient method, hybrid steepest-descent method, and Mann’s iteration method. We prove 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 inclusions, and the solution set of general system of variational inequalities (GSVI), 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 for solving a hierarchical variational inequality problem with constraints of finitely many GMEPs, finitely many variational inclusions, and the GSVI. The results obtained in this paper improve and extend the corresponding results announced by many others.http://dx.doi.org/10.1155/2015/980352 |
| spellingShingle | L. C. Ceng A. Latif C. F. Wen A. E. Al-Mazrooei Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities Journal of Function Spaces |
| title | Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities |
| title_full | Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities |
| title_fullStr | Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities |
| title_full_unstemmed | Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities |
| title_short | Hybrid Steepest-Descent Methods for Triple Hierarchical Variational Inequalities |
| title_sort | hybrid steepest descent methods for triple hierarchical variational inequalities |
| url | http://dx.doi.org/10.1155/2015/980352 |
| work_keys_str_mv | AT lcceng hybridsteepestdescentmethodsfortriplehierarchicalvariationalinequalities AT alatif hybridsteepestdescentmethodsfortriplehierarchicalvariationalinequalities AT cfwen hybridsteepestdescentmethodsfortriplehierarchicalvariationalinequalities AT aealmazrooei hybridsteepestdescentmethodsfortriplehierarchicalvariationalinequalities |