{"title":"Proximal Subgradient Algorithm for a Class of Nonconvex Bilevel Equilibrium Problems","authors":"","doi":"10.1007/s40840-024-01664-w","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we propose an algorithm for a bilevel problem of solving a monotone equilibrium problem over the solution set of a mixed equilibrium problem involving prox-convex functions in finite dimensional Euclidean space <span> <span>\\(\\mathbb R^n\\)</span> </span>. The proposed algorithm is based on the proximal method for mixed variational inequalities by using proximal operators of prox-convex functions. The convergence of the sequences generated by the proposed algorithm is established. Furthermore, some consequences of the main result are given. Finally, we provide numerical examples to illustrate our algorithm;s convergence and compare it with others. As an application, we apply the proposed algorithm to solve a modified oligopolistic Nash–Cournot equilibrium model. </p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"175 1","pages":""},"PeriodicalIF":1.0000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Malaysian Mathematical Sciences Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40840-024-01664-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we propose an algorithm for a bilevel problem of solving a monotone equilibrium problem over the solution set of a mixed equilibrium problem involving prox-convex functions in finite dimensional Euclidean space \(\mathbb R^n\). The proposed algorithm is based on the proximal method for mixed variational inequalities by using proximal operators of prox-convex functions. The convergence of the sequences generated by the proposed algorithm is established. Furthermore, some consequences of the main result are given. Finally, we provide numerical examples to illustrate our algorithm;s convergence and compare it with others. As an application, we apply the proposed algorithm to solve a modified oligopolistic Nash–Cournot equilibrium model.
期刊介绍：
This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.
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