求解Hilbert空间中不动点约束变分不等式的混合惯性收缩算法

IF 0.3 Q4 MATHEMATICS

Acta Mathematica Vietnamica Pub Date : 2022-01-28 DOI:10.1007/s40306-021-00467-6

Pham Ngoc Anh

{"title":"求解Hilbert空间中不动点约束变分不等式的混合惯性收缩算法","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":"{\"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}","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

摘要

本文在前向-后向方法和惯性技术的基础上，提出了一种求解非扩张映射不动点集上的变分不等式问题的新算法。在强单调和Lipschitz连续假设下，建立了算法的强收敛性。作为一个应用，我们还应用并分析了我们的算法来解决两个凸函数之和的凸最小化问题。

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

Hybrid Inertial Contraction Algorithms for Solving Variational Inequalities with Fixed Point Constraints in Hilbert Spaces

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.

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.