Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations

doi:10.1007/s11425-019-9757-0

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	Metrically regular mappings and its application to convergence analysis of a confined Newton-type method for nonsmooth generalized equations
	Rashid, Mohammed Harunor 1,2; Yuan, Ya-xiang 1
	2019-12-02
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
页码	22
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.
关键词	set-valued mappings generalized equations metrically regular mapping semilocal convergence point-based approximation
DOI	10.1007/s11425-019-9757-0
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000500509000002
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50416
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.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
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.