{"title":"Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces","authors":"Pham Ngoc Anh","doi":"10.1007/s40306-021-00467-6","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, basing on the forward-backward method and inertial techniques, we introduce a new algorithm for solving a variational inequality problem over the fixed point set of a nonexpansive mapping. The strong convergence of the algorithm is established under strongly monotone and Lipschitz continuous assumptions imposed on the cost mapping. As an application, we also apply and analyze our algorithm to solve a convex minimization problem of the sum of two convex functions.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-021-00467-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, basing on the forward-backward method and inertial techniques, we introduce a new algorithm for solving a variational inequality problem over the fixed point set of a nonexpansive mapping. The strong convergence of the algorithm is established under strongly monotone and Lipschitz continuous assumptions imposed on the cost mapping. As an application, we also apply and analyze our algorithm to solve a convex minimization problem of the sum of two convex functions.
期刊介绍:
Acta Mathematica Vietnamica is a peer-reviewed mathematical journal. The journal publishes original papers of high quality in all branches of Mathematics with strong focus on Algebraic Geometry and Commutative Algebra, Algebraic Topology, Complex Analysis, Dynamical Systems, Optimization and Partial Differential Equations.