{"title":"Regularized dynamics for monotone inverse variational inequalities in hilbert spaces","authors":"Pham Ky Anh, Trinh Ngoc Hai","doi":"10.1007/s11081-024-09882-8","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we present a regularized dynamical system method for solving monotone inverse variational inequalities (IVIs) in infinite dimensional Hilbert spaces. It is shown that the corresponding Cauchy problem admits a unique strong global solution, whose limit at infinity exists and solves the given monotone IVI. Then by discretizing the dynamical system, we obtain a class of iterative regularization algorithms with relaxation parameters, which are strongly convergent under quite mild assumptions on the cost operator. Some simple numerical examples, including an infinite dimensional one, are given to illustrate the performance of the proposed algorithms.</p>","PeriodicalId":56141,"journal":{"name":"Optimization and Engineering","volume":"98 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization and Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s11081-024-09882-8","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we present a regularized dynamical system method for solving monotone inverse variational inequalities (IVIs) in infinite dimensional Hilbert spaces. It is shown that the corresponding Cauchy problem admits a unique strong global solution, whose limit at infinity exists and solves the given monotone IVI. Then by discretizing the dynamical system, we obtain a class of iterative regularization algorithms with relaxation parameters, which are strongly convergent under quite mild assumptions on the cost operator. Some simple numerical examples, including an infinite dimensional one, are given to illustrate the performance of the proposed algorithms.
期刊介绍:
Optimization and Engineering is a multidisciplinary journal; its primary goal is to promote the application of optimization methods in the general area of engineering sciences. We expect submissions to OPTE not only to make a significant optimization contribution but also to impact a specific engineering application.
Topics of Interest:
-Optimization: All methods and algorithms of mathematical optimization, including blackbox and derivative-free optimization, continuous optimization, discrete optimization, global optimization, linear and conic optimization, multiobjective optimization, PDE-constrained optimization & control, and stochastic optimization. Numerical and implementation issues, optimization software, benchmarking, and case studies.
-Engineering Sciences: Aerospace engineering, biomedical engineering, chemical & process engineering, civil, environmental, & architectural engineering, electrical engineering, financial engineering, geosciences, healthcare engineering, industrial & systems engineering, mechanical engineering & MDO, and robotics.