{"title":"A new relaxed projection and its applications","authors":"Q. Dong, KE S.H., HE S., X. Qin","doi":"10.23952/jnfa.2021.19","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a new relaxed projection onto the level sets of the convex functions. We propose new relaxed projection methods by applying the proposed relaxed projection to solve split feasibility problems and split equality problems. The weak convergence of the relaxed projection methods is established. A preliminary numerical experiment is presented to support the new relaxed projection.","PeriodicalId":44514,"journal":{"name":"Journal of Nonlinear Functional Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-01-01","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.2021.19","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
In this paper, we introduce a new relaxed projection onto the level sets of the convex functions. We propose new relaxed projection methods by applying the proposed relaxed projection to solve split feasibility problems and split equality problems. The weak convergence of the relaxed projection methods is established. A preliminary numerical experiment is presented to support the new relaxed projection.
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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