Vitaliano de Sousa Amaral, Paulo Sérgio Marques dos Santos, Gilson N. Silva, Sissy Souza
{"title":"A MODIFIED NEWTON-SECANT METHOD FOR SOLVING NONSMOOTH GENERALIZED EQUATIONS","authors":"Vitaliano de Sousa Amaral, Paulo Sérgio Marques dos Santos, Gilson N. Silva, Sissy Souza","doi":"10.3846/mma.2024.18680","DOIUrl":null,"url":null,"abstract":"In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modelling and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2024.18680","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
