Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings
In real Hilbert spaces, let the CFPP indicate a common fixed-point problem of asymptotically nonexpansive operator and countably many nonexpansive operators, and suppose that the HVI and VIP represent a hierarchical variational inequality and a variational inequality problem, respectively. We put fo...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/6177912 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849684446044749824 |
|---|---|
| author | Yun-Ling Cui Lu-Chuan Ceng Fang-Fei Zhang Liang He Jie Yin Cong-Shan Wang Hui-Ying Hu |
| author_facet | Yun-Ling Cui Lu-Chuan Ceng Fang-Fei Zhang Liang He Jie Yin Cong-Shan Wang Hui-Ying Hu |
| author_sort | Yun-Ling Cui |
| collection | DOAJ |
| description | In real Hilbert spaces, let the CFPP indicate a common fixed-point problem of asymptotically nonexpansive operator and countably many nonexpansive operators, and suppose that the HVI and VIP represent a hierarchical variational inequality and a variational inequality problem, respectively. We put forward Mann hybrid deepest-descent extragradient approach for solving the HVI with the CFPP and VIP constraints. The proposed algorithms are on the basis of Mann’s iterative technique, viscosity approximation method, subgradient extragradient rule with linear-search process, and hybrid deepest-descent rule. Under suitable restrictions, it is shown that the sequences constructed by the algorithms converge strongly to a solution of the HVI with the CFPP and VIP constraints. |
| format | Article |
| id | doaj-art-c1e9ccaaba344080bc1f53d93d0eee4b |
| institution | DOAJ |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c1e9ccaaba344080bc1f53d93d0eee4b2025-08-20T03:23:27ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/6177912Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive MappingsYun-Ling Cui0Lu-Chuan Ceng1Fang-Fei Zhang2Liang He3Jie Yin4Cong-Shan Wang5Hui-Ying Hu6Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn real Hilbert spaces, let the CFPP indicate a common fixed-point problem of asymptotically nonexpansive operator and countably many nonexpansive operators, and suppose that the HVI and VIP represent a hierarchical variational inequality and a variational inequality problem, respectively. We put forward Mann hybrid deepest-descent extragradient approach for solving the HVI with the CFPP and VIP constraints. The proposed algorithms are on the basis of Mann’s iterative technique, viscosity approximation method, subgradient extragradient rule with linear-search process, and hybrid deepest-descent rule. Under suitable restrictions, it is shown that the sequences constructed by the algorithms converge strongly to a solution of the HVI with the CFPP and VIP constraints.http://dx.doi.org/10.1155/2023/6177912 |
| spellingShingle | Yun-Ling Cui Lu-Chuan Ceng Fang-Fei Zhang Liang He Jie Yin Cong-Shan Wang Hui-Ying Hu Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings Journal of Mathematics |
| title | Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings |
| title_full | Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings |
| title_fullStr | Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings |
| title_full_unstemmed | Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings |
| title_short | Mann Hybrid Deepest-Descent Extragradient Method with Line-Search Process for Hierarchical Variational Inequalities for Countable Nonexpansive Mappings |
| title_sort | mann hybrid deepest descent extragradient method with line search process for hierarchical variational inequalities for countable nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2023/6177912 |
| work_keys_str_mv | AT yunlingcui mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings AT luchuanceng mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings AT fangfeizhang mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings AT lianghe mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings AT jieyin mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings AT congshanwang mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings AT huiyinghu mannhybriddeepestdescentextragradientmethodwithlinesearchprocessforhierarchicalvariationalinequalitiesforcountablenonexpansivemappings |