一般变分不等式:解的存在性、tikhonov型正则化和适定性

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2021-07-06 DOI:10.1007/s40306-021-00435-0

Tran Van Nghi, Nguyen Nang Tam

{"title":"一般变分不等式:解的存在性、tikhonov型正则化和适定性","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":"{\"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}","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

摘要

本文给出了一般变分不等式解存在唯一性的充要条件。提出了一种求解GVI的Tikhonov型正则化方法。最后，在适当的条件下，我们证明了GVI的适定性等价于解的存在唯一性。将所得结果与以前的结果进行了比较。特别地，我们的结果推广了反变分不等式的相应结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

General Variational Inequalities: Existence of Solutions, Tikhonov-Type Regularization, and Well-posedness

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Acta Mathematica Vietnamica MATHEMATICS-

CiteScore

0.90

自引率

0.00%

发文量

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.