Construction algorithms for a class of monotone variational inequalities

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• 作者：Yonghong Yao ; Mihai Postolache ; Yeong-Cheng Liou ; Zhangsong Yao
• 关键词：Variational inequality ; Monotone operator ; Nonexpansive operator ; Implicit algorithm
• 刊名：Optimization Letters
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：10
• 期：7
• 页码：1519-1528
• 全文大小：381 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operation Research and Decision Theory
  Numerical and Computational Methods in Engineering
  Numerical and Computational Methods
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1862-4480
• 卷排序：10

文摘

This paper is devoted to solve the following monotone variational inequality of finding \(x^*\in \mathrm{Fix}(T)\) such that $$\begin{aligned} \langle Ax^*,x-x^*\rangle \ge 0,\quad \forall x\in \mathrm{Fix}(T), \end{aligned}$$where A is a monotone operator and \(\mathrm{Fix}(T)\) is the set of fixed points of nonexpansive operator T. For this purpose, we construct an implicit algorithm and prove its convergence hierarchical to the solution of above monotone variational inequality.KeywordsVariational inequalityMonotone operatorNonexpansive operatorImplicit algorithmReferences1.Stampacchia, G.: Formes bilineaires coercivites sur les ensembles convexes. C. R. Acad. Sci. Paris. 258, 4413–4416 (1964)MathSciNetMATHGoogle Scholar2.Korpelevich, G.M.: An extragradient method for finding saddle points and for other problems. Ekon. Mat. Metody. 12, 747–756 (1976)MathSciNetMATHGoogle Scholar3.Glowinski, R.: Numerical Methods for Nonlinear Variational Problems. 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Math. 13, 365–374 (1974)MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer-Verlag Berlin Heidelberg 2015Authors and AffiliationsYonghong Yao1Mihai Postolache2Email authorYeong-Cheng Liou34Zhangsong Yao51.Department of MathematicsTianjin Polytechnic UniversityTianjinChina2.Faculty of Applied SciencesUniversity “Politehnica” of BucharestBucharestRomania3.Department of Information ManagementCheng Shiu UniversityKaohsiungTaiwan4.Center for General EducationKaohsiung Medical UniversityKaohsiungTaiwan5.School of Information EngineeringNanjing Xiaozhuang UniversityNanjingChina About this article CrossMark Print ISSN 1862-4472 Online ISSN 1862-4480 Publisher Name Springer Berlin Heidelberg About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s11590-015-0954-8_Construction algorithms for a clas", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s11590-015-0954-8_Construction algorithms for a clas", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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