Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality
Abstract This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem constraint of finitely many nonexpansive mappings. The problem under consideration...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-02913-5 |
| _version_ | 1811175718517735424 |
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| author | Lu-Chuan Ceng Debdas Ghosh Yekini Shehu Jen-Chih Yao |
| author_facet | Lu-Chuan Ceng Debdas Ghosh Yekini Shehu Jen-Chih Yao |
| author_sort | Lu-Chuan Ceng |
| collection | DOAJ |
| description | Abstract This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem constraint of finitely many nonexpansive mappings. The problem under consideration is in real Hilbert spaces, where the BSPVIP involves a fixed point problem of demimetric mapping. The proposed rule exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established under some suitable assumptions. In addition, a numerical example is given to demonstrate the viability of the proposed rule. Our results improve and extend some recent developments to a great extent. |
| first_indexed | 2024-04-10T19:40:20Z |
| format | Article |
| id | doaj.art-e0d9304f1faf42d385b5384d95ddfd28 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-10T19:40:20Z |
| publishDate | 2023-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-e0d9304f1faf42d385b5384d95ddfd282023-01-29T12:24:27ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-01-012023112210.1186/s13660-023-02913-5Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequalityLu-Chuan Ceng0Debdas Ghosh1Yekini Shehu2Jen-Chih Yao3Department of Mathematics, Shanghai Normal UniversityDepartment of Mathematical Sciences, Indian Institute of Technology (BHU)College of Mathematics and Computer Science, Zhejiang Normal UniversityResearch Center for Interneural Computing, China Medical University Hospital, China Medical UniversityAbstract This paper introduces a triple-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality problem (BSPVIP) with the common fixed point problem constraint of finitely many nonexpansive mappings. The problem under consideration is in real Hilbert spaces, where the BSPVIP involves a fixed point problem of demimetric mapping. The proposed rule exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established under some suitable assumptions. In addition, a numerical example is given to demonstrate the viability of the proposed rule. Our results improve and extend some recent developments to a great extent.https://doi.org/10.1186/s13660-023-02913-5Subgradient extragradient processBilevel split pseudomonotone variational inequality problemExtrapolation stepDemimetric mappingFixed pointNonexpansive mapping |
| spellingShingle | Lu-Chuan Ceng Debdas Ghosh Yekini Shehu Jen-Chih Yao Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality Journal of Inequalities and Applications Subgradient extragradient process Bilevel split pseudomonotone variational inequality problem Extrapolation step Demimetric mapping Fixed point Nonexpansive mapping |
| title | Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality |
| title_full | Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality |
| title_fullStr | Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality |
| title_full_unstemmed | Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality |
| title_short | Triple-adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality |
| title_sort | triple adaptive subgradient extragradient with extrapolation procedure for bilevel split variational inequality |
| topic | Subgradient extragradient process Bilevel split pseudomonotone variational inequality problem Extrapolation step Demimetric mapping Fixed point Nonexpansive mapping |
| url | https://doi.org/10.1186/s13660-023-02913-5 |
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