Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems
This paper considers an alternated inertial-type extrapolation algorithm for solving bilevel pseudomonotone variational inequality problem in the framework of real Hilbert spaces with split variational inequality and fixed-point constraints of demimetric mapping. The algorithm which involves alterna...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/3185746 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547828216365056 |
|---|---|
| author | Jacob Ashiwere Abuchu Austine Efut Ofem Godwin Chidi Ugwunnadi Ojen Kumar Narain Azhar Hussain |
| author_facet | Jacob Ashiwere Abuchu Austine Efut Ofem Godwin Chidi Ugwunnadi Ojen Kumar Narain Azhar Hussain |
| author_sort | Jacob Ashiwere Abuchu |
| collection | DOAJ |
| description | This paper considers an alternated inertial-type extrapolation algorithm for solving bilevel pseudomonotone variational inequality problem in the framework of real Hilbert spaces with split variational inequality and fixed-point constraints of demimetric mapping. The algorithm which involves alternated inertial uses self-adjustment stepsize condition that depends solely on the information from previous iterative step. The bilevel problem considered in the work consists of upper-level problem with an underlying operator which is pseudomonotone, while the lower problem is associated with strongly monotone mapping and the fixed-point constraint of demimetric mapping. Our algorithm is anchored on modified projection and contraction techniques, fused with alternated inertial and relaxation. Under some suitable conditions on the algorithm control parameters, we obtain a strong convergence result of the proposed method without the prior knowledge of the operator norm or the coefficients of the underlying operators within the scope of real Hilbert spaces. Finally, some numerical examples are presented to illustrate the gain of our method in comparison to some related algorithms in the literature. |
| format | Article |
| id | doaj-art-20e4e1fe2e03448296525324d430d523 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-20e4e1fe2e03448296525324d430d5232025-02-03T06:43:13ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/3185746Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality ProblemsJacob Ashiwere Abuchu0Austine Efut Ofem1Godwin Chidi Ugwunnadi2Ojen Kumar Narain3Azhar Hussain4School of MathematicsSchool of MathematicsDepartment of MathematicsSchool of MathematicsDepartment of MathematicsThis paper considers an alternated inertial-type extrapolation algorithm for solving bilevel pseudomonotone variational inequality problem in the framework of real Hilbert spaces with split variational inequality and fixed-point constraints of demimetric mapping. The algorithm which involves alternated inertial uses self-adjustment stepsize condition that depends solely on the information from previous iterative step. The bilevel problem considered in the work consists of upper-level problem with an underlying operator which is pseudomonotone, while the lower problem is associated with strongly monotone mapping and the fixed-point constraint of demimetric mapping. Our algorithm is anchored on modified projection and contraction techniques, fused with alternated inertial and relaxation. Under some suitable conditions on the algorithm control parameters, we obtain a strong convergence result of the proposed method without the prior knowledge of the operator norm or the coefficients of the underlying operators within the scope of real Hilbert spaces. Finally, some numerical examples are presented to illustrate the gain of our method in comparison to some related algorithms in the literature.http://dx.doi.org/10.1155/2023/3185746 |
| spellingShingle | Jacob Ashiwere Abuchu Austine Efut Ofem Godwin Chidi Ugwunnadi Ojen Kumar Narain Azhar Hussain Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems Journal of Mathematics |
| title | Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems |
| title_full | Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems |
| title_fullStr | Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems |
| title_full_unstemmed | Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems |
| title_short | Hybrid Alternated Inertial Projection and Contraction Algorithm for Solving Bilevel Variational Inequality Problems |
| title_sort | hybrid alternated inertial projection and contraction algorithm for solving bilevel variational inequality problems |
| url | http://dx.doi.org/10.1155/2023/3185746 |
| work_keys_str_mv | AT jacobashiwereabuchu hybridalternatedinertialprojectionandcontractionalgorithmforsolvingbilevelvariationalinequalityproblems AT austineefutofem hybridalternatedinertialprojectionandcontractionalgorithmforsolvingbilevelvariationalinequalityproblems AT godwinchidiugwunnadi hybridalternatedinertialprojectionandcontractionalgorithmforsolvingbilevelvariationalinequalityproblems AT ojenkumarnarain hybridalternatedinertialprojectionandcontractionalgorithmforsolvingbilevelvariationalinequalityproblems AT azharhussain hybridalternatedinertialprojectionandcontractionalgorithmforsolvingbilevelvariationalinequalityproblems |