{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:41:02Z","timestamp":1759970462595,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:00:00Z","timestamp":1737504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Jiagen Liao of Science Foundation of Hubei Provincial Department of Education","award":["Q20231210","11871383"],"award-info":[{"award-number":["Q20231210","11871383"]}]},{"name":"Zhongping Wan of Natural Science Foundation of China","award":["Q20231210","11871383"],"award-info":[{"award-number":["Q20231210","11871383"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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\u2019s 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.<\/jats:p>","DOI":"10.3390\/axioms14020078","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T03:40:17Z","timestamp":1737517217000},"page":"78","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Korpelevich Method for Solving Bilevel Variational Inequalities on Riemannian Manifolds"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3058-8549","authenticated-orcid":false,"given":"Jiagen","family":"Liao","sequence":"first","affiliation":[{"name":"Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China"},{"name":"College of Mathematics and Physics, China Three Gorges University, Yichang 443002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhongping","family":"Wan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1016\/S0362-546X(02)00266-3","article-title":"Variational inequalities on Hadamard manifolds","volume":"52","year":"2003","journal-title":"Nonlinear Anal. 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