一类变分不等式的一阶动力系统及其离散化

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2024-10-28 DOI:10.1016/j.cam.2024.116341

Nguyen Buong

{"title":"一类变分不等式的一阶动力系统及其离散化","authors":"Nguyen Buong","doi":"10.1016/j.cam.2024.116341","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.</div></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":"458 ","pages":"Article 116341"},"PeriodicalIF":2.1000,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A first order dynamical system and its discretization for a class of variational inequalities\",\"authors\":\"Nguyen Buong\",\"doi\":\"10.1016/j.cam.2024.116341\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.</div></div>\",\"PeriodicalId\":50226,\"journal\":{\"name\":\"Journal of Computational and Applied Mathematics\",\"volume\":\"458 \",\"pages\":\"Article 116341\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0377042724005892\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005892","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们研究了实希尔伯特空间上一个利普齐兹连续伪收缩和一个有限族严格伪收缩算子的公共定点集合上的变分不等式问题。我们根据拉夫连季耶夫正则化方法引入了一阶动力系统。在一些温和的条件下，证明了该动力学系统轨迹离散化变体的存在性和强收敛性。为了验证我们的结果，还给出了解决凸约束单调方程和 LASSO 问题的数值实验应用。

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

A first order dynamical system and its discretization for a class of variational inequalities

In this paper, we study the variational inequality problem over the set of common fixed points of a Lipschitz continuous pseudo-contraction and a finite family of strictly pseudo-contractive operators on a real Hilbert space. We introduce a first order dynamical system in accordance with the Lavrentiev regularization method. The existence and strong convergence with a discretized variant of the trajectory of the dynamical system are proved under some mild conditions. Applications to solving the convex constrained monotone equations and to the LASSO problem with numerical experiments are given for validating our results.

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

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.