{"title":"Strong convergence of Multi-parameter Projection Methods for variational inequality Problems","authors":"D. Hieu, L. Muu, Pham Kim Quy","doi":"10.3846/mma.2022.14479","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a multi-parameter projection method for solving a variational inequality problem, and establish its strong convergence in a Hilbert space under appropriate conditions. The method involves two projectionsteps with different variable stepsizes where one of them is computed explicitly on a specifically structural half-space. The proof of strong convergence of the method is based on the regularization solutions depending on parameters of the original problem. It turns out that the solution obtained by the method is the solution of a bilevel variational inequality problem whose constraint is the solution set of our considered problem. In order to support the obtained theoretical results, we perform some experiments on transportation equilibrium and optimal control problems, and also involve comparisons. Numerical results show the computational effectiveness and the fast convergence of the new method over some existing ones.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2022.14479","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce a multi-parameter projection method for solving a variational inequality problem, and establish its strong convergence in a Hilbert space under appropriate conditions. The method involves two projectionsteps with different variable stepsizes where one of them is computed explicitly on a specifically structural half-space. The proof of strong convergence of the method is based on the regularization solutions depending on parameters of the original problem. It turns out that the solution obtained by the method is the solution of a bilevel variational inequality problem whose constraint is the solution set of our considered problem. In order to support the obtained theoretical results, we perform some experiments on transportation equilibrium and optimal control problems, and also involve comparisons. Numerical results show the computational effectiveness and the fast convergence of the new method over some existing ones.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.