Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds
The bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korpelevich’s method specifically designed for solving...
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MDPI AG
2025-01-01
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| author | Jiagen Liao Zhongping Wan |
| author_facet | Jiagen Liao Zhongping Wan |
| author_sort | Jiagen Liao |
| collection | DOAJ |
| description | The bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korpelevich’s method specifically designed for solving bilevel variational inequalities on Riemannian manifolds with nonnegative sectional curvature and pseudomonotone vector fields. This variant aims to find a solution that satisfies certain conditions. Through our proposed algorithm, we are able to generate iteration sequences that converge to a solution, given mild conditions. Finally, we provide an example to demonstrate the effectiveness of our algorithm. |
| format | Article |
| id | doaj-art-3766d01c5a3c4b72beda7240fe36a2ed |
| institution | DOAJ |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-3766d01c5a3c4b72beda7240fe36a2ed2025-08-20T03:12:12ZengMDPI AGAxioms2075-16802025-01-011427810.3390/axioms14020078Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian ManifoldsJiagen Liao0Zhongping Wan1Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan 430072, ChinaThe bilevel variational inequality on Riemannian manifolds refers to a mathematical problem involving the interaction between two levels of optimization, where one level is constrained by the other level. In this context, we present a variant of Korpelevich’s method specifically designed for solving bilevel variational inequalities on Riemannian manifolds with nonnegative sectional curvature and pseudomonotone vector fields. This variant aims to find a solution that satisfies certain conditions. Through our proposed algorithm, we are able to generate iteration sequences that converge to a solution, given mild conditions. Finally, we provide an example to demonstrate the effectiveness of our algorithm.https://www.mdpi.com/2075-1680/14/2/78Riemannian manifoldsbilevel variational inequalitiespseudomonotone vector fieldsextragradient method |
| spellingShingle | Jiagen Liao Zhongping Wan Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds Axioms Riemannian manifolds bilevel variational inequalities pseudomonotone vector fields extragradient method |
| title | Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds |
| title_full | Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds |
| title_fullStr | Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds |
| title_full_unstemmed | Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds |
| title_short | Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds |
| title_sort | korpelevich method for solving bilevel variational inequalities on riemannian manifolds |
| topic | Riemannian manifolds bilevel variational inequalities pseudomonotone vector fields extragradient method |
| url | https://www.mdpi.com/2075-1680/14/2/78 |
| work_keys_str_mv | AT jiagenliao korpelevichmethodforsolvingbilevelvariationalinequalitiesonriemannianmanifolds AT zhongpingwan korpelevichmethodforsolvingbilevelvariationalinequalitiesonriemannianmanifolds |