Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints
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 s...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/767109 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849306015344885760 |
|---|---|
| author | Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen |
| author_facet | Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-30f408ebb7524e3195754cfd331cc0f0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-30f408ebb7524e3195754cfd331cc0f02025-08-20T03:55:12ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/767109767109Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization ConstraintsLu-Chuan Ceng0Cheng-Wen Liao1Chin-Tzong Pang2Ching-Feng Wen3Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, ChinaDepartment of Food and Beverage Management, Vanung University, Chung-Li 320061, TaiwanDepartment of Information Management, Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li 32003, TaiwanCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanWe 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.http://dx.doi.org/10.1155/2014/767109 |
| spellingShingle | Lu-Chuan Ceng Cheng-Wen Liao Chin-Tzong Pang Ching-Feng Wen Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints Abstract and Applied Analysis |
| title | Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints |
| title_full | Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints |
| title_fullStr | Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints |
| title_full_unstemmed | Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints |
| title_short | Hybrid Iterative Scheme for Triple Hierarchical Variational Inequalities with Mixed Equilibrium, Variational Inclusion, and Minimization Constraints |
| title_sort | hybrid iterative scheme for triple hierarchical variational inequalities with mixed equilibrium variational inclusion and minimization constraints |
| url | http://dx.doi.org/10.1155/2014/767109 |
| work_keys_str_mv | AT luchuanceng hybriditerativeschemefortriplehierarchicalvariationalinequalitieswithmixedequilibriumvariationalinclusionandminimizationconstraints AT chengwenliao hybriditerativeschemefortriplehierarchicalvariationalinequalitieswithmixedequilibriumvariationalinclusionandminimizationconstraints AT chintzongpang hybriditerativeschemefortriplehierarchicalvariationalinequalitieswithmixedequilibriumvariationalinclusionandminimizationconstraints AT chingfengwen hybriditerativeschemefortriplehierarchicalvariationalinequalitieswithmixedequilibriumvariationalinclusionandminimizationconstraints |