KMS Of Academy of mathematics and systems sciences, CAS
| Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings | |
| Rashid, M. H.1,2; Yuan, Ya-xiang1 | |
| 2022-01-02 | |
| Source Publication | APPLICABLE ANALYSIS
 |
| ISSN | 0003-6811 |
| Volume | 101Issue:1Pages:14-34 |
| Abstract | Let X and Y be Banach spaces. Let f : X -> Y be a Frechet differentiable function and F: X paired right arrows 2(Y) be a set-valued mapping with closed graph. In this paper, a restricted Newton-type method has been introduced for solving the generalized equations of the form 0 is an element of f(x) + F(x). Under some suitable conditions, we will establish the convergence criteria of the restricted Newton-type method, which ensures the existence and the convergence of any sequence generated by this method. More precisely, when the Frechet derivative of f is continuous and Lipschitz continuous as well as f + F is metrically regular, we analyze the semilocal and local convergence of the restricted Newton-type method. In addition, an example is given to show the reason for considering the metrically regular property instead of Lipschitz-like property of set-valued mapping in this paper. |
| Keyword | Generalized equation set-valued mappings metrically regular mappings restricted Newton-type method semi-local convergence |
| DOI | 10.1080/00036811.2017.1392018 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | CAS-President International Fellowship Initiative(PIFI), Chinese Academy of Sciences, China ; National Natural Science Foundation of China[11331012] ; National Natural Science Foundation of China[11321061] ; National Natural Science Foundation of China[11461161005] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000764570600002 |
| Publisher | TAYLOR & FRANCIS LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60143 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Rashid, M. H. |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing, Peoples R China 2.Univ Rajshahi, Fac Sci, Dept Math, Rajshahi, Bangladesh |
| Recommended Citation GB/T 7714 | Rashid, M. H.,Yuan, Ya-xiang. Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings[J]. APPLICABLE ANALYSIS,2022,101(1):14-34. |
| APA | Rashid, M. H.,&Yuan, Ya-xiang.(2022).Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings.APPLICABLE ANALYSIS,101(1),14-34. |
| MLA | Rashid, M. H.,et al."Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings".APPLICABLE ANALYSIS 101.1(2022):14-34. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment