Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations
文献类型：期刊论文
| 作者 | Rashid, Mohammed Harunor1,2; Yuan, Ya-xiang2 |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2019-12-02 |
| 页码 | 22 |
| 关键词 | set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-019-9757-0 |
| 英文摘要 | 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. |
| 资助项目 | 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研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000500509000002 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50415]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Rashid, Mohammed Harunor |
| 作者单位 | 1.Univ Rajshahi, Dept Math, Fac Sci, Rajshahi 6205, Bangladesh 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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