S. S. Ablaev, F. S. Stonyakin, M. S. Alkousa, D. A. Pasechnyk
{"title":"Adaptive Methods for Variational Inequalities with Relatively Smooth and Reletively Strongly Monotone Operators","authors":"S. S. Ablaev, F. S. Stonyakin, M. S. Alkousa, D. A. Pasechnyk","doi":"10.1134/s0361768823060026","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Based on the recently proposed proximal version of the extragradient method for this class of problems, we study in detail the method with adaptively selected parameter values. The rate of convergence of this method is estimated. The result is generalized to the class of variational inequalities with relatively strongly monotone δ-generalized smooth operators. For the ridge regression problem and variational inequality associated with box-simplex games, numerical experiments are carried out to demonstrate the effectiveness of the proposed technique for adaptive parameter selection during the execution of the algorithm.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":"20 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Programming and Computer Software","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s0361768823060026","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is devoted to some adaptive methods for variational inequalities with relatively smooth and relatively strongly monotone operators. Based on the recently proposed proximal version of the extragradient method for this class of problems, we study in detail the method with adaptively selected parameter values. The rate of convergence of this method is estimated. The result is generalized to the class of variational inequalities with relatively strongly monotone δ-generalized smooth operators. For the ridge regression problem and variational inequality associated with box-simplex games, numerical experiments are carried out to demonstrate the effectiveness of the proposed technique for adaptive parameter selection during the execution of the algorithm.
期刊介绍：
Programming and Computer Software is a peer reviewed journal devoted to problems in all areas of computer science: operating systems, compiler technology, software engineering, artificial intelligence, etc.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
