A nonmonotone inexact Newton method for unconstrained optimization

doi:10.1007/s11590-015-0976-2

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	A nonmonotone inexact Newton method for unconstrained optimization
	Gao, Huan 1; Zhang, Hai-Bin 1; Li, Zhi-Bao 2; Tadjouddine, Emmanuel 3
	2017-06-01
发表期刊	OPTIMIZATION LETTERS
ISSN	1862-4472
卷号	11 期号:5 页码:947-965
摘要	It is well known that the Newton method has a second order rate of convergence and that it is widely used to solve optimization problems and nonlinear equations which arise from computational science, engineering analysis and other applications. However, two big disadvantages hinder its application: high computational cost for large scale problems and poor global performance in some complicated and difficult problems. Some inexact Newton methods have emerged over time. Among them, the Newton preconditioned conjugate gradient method is the most efficient and popular approach to overcome the first shortcoming while keeping rapid convergence. In this paper, we have improved the global performance of the inexact Newton method by developing a nonmonotone line search technique. We have also proved the global convergence of the proposed method under some conditions. Numerical experiments on a set of standard test problems are reported. They have shown that the proposed algorithm is promising.
关键词	Inexact Newton method Nonmonotone line search Preconditioned conjugate gradient Global convergence
DOI	10.1007/s11590-015-0976-2
语种	英语
资助项目	National Natural Science Foundation of China[61179033] ; Collaborative Innovation Center on Beijing Society-building and Social Governance ; China Postdoctoral Science Foundation[2014M561081]
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000401258300005
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/25361
专题	中国科学院数学与系统科学研究院
通讯作者	Gao, Huan
作者单位	1.Beijing Univ Technol, Coll Appl Sci, Beijing, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing, Peoples R China 3.Xian Jiaotong Liverpool Univ, Comp Sci & Software Engn, SIP, Suzhou, Peoples R China
推荐引用方式 GB/T 7714	Gao, Huan,Zhang, Hai-Bin,Li, Zhi-Bao,et al. A nonmonotone inexact Newton method for unconstrained optimization[J]. OPTIMIZATION LETTERS,2017,11(5):947-965.
APA	Gao, Huan,Zhang, Hai-Bin,Li, Zhi-Bao,&Tadjouddine, Emmanuel.(2017).A nonmonotone inexact Newton method for unconstrained optimization.OPTIMIZATION LETTERS,11(5),947-965.
MLA	Gao, Huan,et al."A nonmonotone inexact Newton method for unconstrained optimization".OPTIMIZATION LETTERS 11.5(2017):947-965.