Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings

doi:10.1080/00036811.2017.1392018

	Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings
	Rashid, M. H.1,2; Yuan, Ya-xiang 2
刊名	APPLICABLE ANALYSIS
	2022-01-02
卷号	101 期号:1 页码:14-34
关键词	Generalized equation set-valued mappings metrically regular mappings restricted Newton-type method semi-local convergence
ISSN号	0003-6811
DOI	10.1080/00036811.2017.1392018
英文摘要	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.
资助项目	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研究方向	Mathematics
语种	英语
出版者	TAYLOR & FRANCIS LTD
WOS记录号	WOS:000764570600002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60142]
专题	中国科学院数学与系统科学研究院
通讯作者	Rashid, M. H.
作者单位	1.Univ Rajshahi, Fac Sci, Dept Math, Rajshahi, Bangladesh 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci Engn Comp, Beijing, Peoples R China
推荐引用方式 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.