{"title":"General Variational Inequalities: Existence of Solutions, Tikhonov-Type Regularization, and Well-posedness","authors":"Tran Van Nghi, Nguyen Nang Tam","doi":"10.1007/s40306-021-00435-0","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we present necessary and sufficient conditions for existence and uniqueness of solutions of general variational inequalities (GVIs). A Tikhonov-type regularization method to find a solution of GVIs is proposed. Finally, under suitable conditions, we prove that the well-posedness of a GVI is equivalent to the solution existence and uniqueness. The obtained results are compared with the previous ones. In particular, our results generalize corresponding ones for inverse variational inequalities.</p></div>","PeriodicalId":45527,"journal":{"name":"Acta Mathematica Vietnamica","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40306-021-00435-0","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Vietnamica","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40306-021-00435-0","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: 4
Abstract
In this paper, we present necessary and sufficient conditions for existence and uniqueness of solutions of general variational inequalities (GVIs). A Tikhonov-type regularization method to find a solution of GVIs is proposed. Finally, under suitable conditions, we prove that the well-posedness of a GVI is equivalent to the solution existence and uniqueness. The obtained results are compared with the previous ones. In particular, our results generalize corresponding ones for inverse variational inequalities.
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.