{"title":"弱条件下广义方程的牛顿法","authors":"I. Argyros, S. George","doi":"10.55630/serdica.2023.49.269-282","DOIUrl":null,"url":null,"abstract":"A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.","PeriodicalId":509503,"journal":{"name":"Serdica Mathematical Journal","volume":"29 7","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Newton's method for generalized equations under weak conditions\",\"authors\":\"I. Argyros, S. George\",\"doi\":\"10.55630/serdica.2023.49.269-282\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.\",\"PeriodicalId\":509503,\"journal\":{\"name\":\"Serdica Mathematical Journal\",\"volume\":\"29 7\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Serdica Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.55630/serdica.2023.49.269-282\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Serdica Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.55630/serdica.2023.49.269-282","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Newton's method for generalized equations under weak conditions
A local convergence analysis is developed for Newton’s method in order to approximate a solution of a generalized equations in a Banach space setting. The convergence conditions are based on generalized continuity conditions on the Fr´echet derivative of the operator involved and the Aubin property. The specialized cases of our results extend earlier ones using similar information.
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