{"title":"Three-Step Approximation Methods from Continuous and Discrete Perspective for Quasi-Variational Inequalities","authors":"N. Mijajlović, M. Jaćimović","doi":"10.1134/s0965542524700027","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The objective of this manuscript is to study the convergence of three-step approximation methods for quasi-variational inequalities in the general case. First, we propose the three-step dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into a three-step iterative method, which we prove to converge also when it is applied to strongly-monotone quasi-variational inequalities. In addition, we show that linear convergence is guaranteed under strong-monotonicity.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700027","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The objective of this manuscript is to study the convergence of three-step approximation methods for quasi-variational inequalities in the general case. First, we propose the three-step dynamical system and carry out an asymptotic analysis for the generated trajectories. The explicit time discretization of this system results into a three-step iterative method, which we prove to converge also when it is applied to strongly-monotone quasi-variational inequalities. In addition, we show that linear convergence is guaranteed under strong-monotonicity.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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