An increasing-angle property of the conjugate gradient method and the implementation of large-scale minimization algorithms with line searches

doi:10.1002/nla.305

	An increasing-angle property of the conjugate gradient method and the implementation of large-scale minimization algorithms with line searches
	Dai, YH; Martinez, JM ; Yuan, JY
	2003-06-01
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN	1070-5325
卷号	10 期号:4 页码:323-334
摘要	The search direction in unconstrained minimization algorithms for large-scale problems is usually computed as an iterate of the preconditioned) conjugate gradient method applied to the minimization of a local quadratic model. In line-search procedures this direction is required to satisfy an angle condition that says that the angle between the negative gradient at the current point and the direction is bounded away from pi/2. In this paper, it is shown that the angle between conjugate gradient iterates and the negative gradient strictly increases as far as the conjugate gradient algorithm proceeds. There is fore, the interruption of the conjugate gradient sub-algorithm when the angle condition does not hold is theoretically justified. Copyright (C) 2002 John Wiley Sons, Ltd.
关键词	conjugate gradients unconstrained minimization truncated Newton methods truncated quasi-Newton methods large scale problems
DOI	10.1002/nla.305
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000183463200003
出版者	JOHN WILEY & SONS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18810
专题	计算数学与科学工程计算研究所
通讯作者	Yuan, JY
作者单位	1.Univ Fed Parana, Dept Math, Ctr Politecn, BR-81531990 Curitiba, Parana, Brazil 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 3.Univ Estadual Campinas, IMECC, Dept Math Appl, BR-13081970 Campinas, SP, Brazil
推荐引用方式 GB/T 7714	Dai, YH,Martinez, JM,Yuan, JY. An increasing-angle property of the conjugate gradient method and the implementation of large-scale minimization algorithms with line searches[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2003,10(4):323-334.
APA	Dai, YH,Martinez, JM,&Yuan, JY.(2003).An increasing-angle property of the conjugate gradient method and the implementation of large-scale minimization algorithms with line searches.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,10(4),323-334.
MLA	Dai, YH,et al."An increasing-angle property of the conjugate gradient method and the implementation of large-scale minimization algorithms with line searches".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 10.4(2003):323-334.