KMS Of Academy of mathematics and systems sciences, CAS
Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations | |
Rashid, Mohammed Harunor1,2; Yuan, Ya-xiang1 | |
2019-12-02 | |
Source Publication | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
Pages | 22 |
Abstract | Notion of metrically regular property and certain types of point-based approximations are used for solving the nonsmooth generalized equation f (x) + F(x) CONTAINS AS MEMBER 0, where X and Y are Banach spaces, and U is an open subset of X, f : U -> Y is a nonsmooth function and F : X Y is a set-valued mapping with closed graph. We introduce a confined Newton-type method for solving the above nonsmooth generalized equation and analyze the semilocal and local convergence of this method. Specifically, under the point-based approximation of f on U and metrically regular property of f + F, we present quadratic rate of convergence of this method. Furthermore, superlinear rate of convergence of this method is provided under the conditions that f admits p-point-based approximation on U and f + F is metrically regular. An example of nonsmooth functions that have p-point-based approximation is given. Moreover, a numerical experiment is given which illustrates the theoretical result. |
Keyword | set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation |
DOI | 10.1007/s11425-019-9757-0 |
Indexed By | SCI |
Language | 英语 |
Funding Project | CAS-President International Fellowship Initiative (PIFI), Chinese Academy of Sciences, Beijing, China ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11331012] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000500509000002 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/50416 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Rashid, Mohammed Harunor |
Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China 2.Univ Rajshahi, Dept Math, Fac Sci, Rajshahi 6205, Bangladesh |
Recommended Citation GB/T 7714 | Rashid, Mohammed Harunor,Yuan, Ya-xiang. Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations[J]. SCIENCE CHINA-MATHEMATICS,2019:22. |
APA | Rashid, Mohammed Harunor,&Yuan, Ya-xiang.(2019).Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations.SCIENCE CHINA-MATHEMATICS,22. |
MLA | Rashid, Mohammed Harunor,et al."Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations".SCIENCE CHINA-MATHEMATICS (2019):22. |
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