{"title":"Linear convergence of an iterative algorithm for solving the split equality mixed equilibrium problem","authors":"","doi":"10.23952/jnfa.2023.14","DOIUrl":null,"url":null,"abstract":". This paper investigates the linear convergence of a projection algorithm for solving the split equality mixed equilibrium problem (SEMEP). We introduce the notion of bounded linear regularity property for the SE-MEP and construct several sufficient conditions to prove its linear convergence. Furthermore, the result of the linear convergence of the SEMEP is applied to split equality equilibrium problems, split equality convex minimization problems, split equality mixed variational inequality problems, and split equality variational inequality problems. Finally, numerical results are provided to verify the effectiveness of our proposed algorithm","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":"1 1","pages":"0"},"PeriodicalIF":1.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nonlinear Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23952/jnfa.2023.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
. This paper investigates the linear convergence of a projection algorithm for solving the split equality mixed equilibrium problem (SEMEP). We introduce the notion of bounded linear regularity property for the SE-MEP and construct several sufficient conditions to prove its linear convergence. Furthermore, the result of the linear convergence of the SEMEP is applied to split equality equilibrium problems, split equality convex minimization problems, split equality mixed variational inequality problems, and split equality variational inequality problems. Finally, numerical results are provided to verify the effectiveness of our proposed algorithm
期刊介绍：
Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.
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