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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
Source PublicationNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
ISSN1070-5325
Volume10Issue:4Pages:323-334
AbstractThe 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.
Keywordconjugate gradients unconstrained minimization truncated Newton methods truncated quasi-Newton methods large scale problems
DOI10.1002/nla.305
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000183463200003
PublisherJOHN WILEY & SONS LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/18810
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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