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A Barzilai-Borwein conjugate gradient method
Dai YuHong1; Kou CaiXia2
2016-08-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume59Issue:8Pages:1511-1524
AbstractThe linear conjugate gradient method is an optimal method for convex quadratic minimization due to the Krylov subspace minimization property. The proposition of limited-memory BFGS method and Barzilai-Borwein gradient method, however, heavily restricted the use of conjugate gradient method for large-scale nonlinear optimization. This is, to the great extent, due to the requirement of a relatively exact line search at each iteration and the loss of conjugacy property of the search directions in various occasions. On the contrary, the limited-memory BFGS method and the Barzilai-Bowein gradient method share the so-called asymptotical one stepsize per line-search property, namely, the trial stepsize in the method will asymptotically be accepted by the line search when the iteration is close to the solution. This paper will focus on the analysis of the subspace minimization conjugate gradient method by Yuan and Stoer (1995). Specifically, if choosing the parameter in the method by combining the Barzilai-Borwein idea, we will be able to provide some efficient Barzilai-Borwein conjugate gradient (BBCG) methods. The initial numerical experiments show that one of the variants, BBCG3, is specially efficient among many others without line searches. This variant of the BBCG method might enjoy the asymptotical one stepsize per line-search property and become a strong candidate for large-scale nonlinear optimization.
Keywordconjugate gradient method subspace minimization Barzilai-Bowein gradient method line search descent property global convergence
DOI10.1007/s11425-016-0279-2
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000380212100005
PublisherSCIENCE PRESS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/23269
Collection计算数学与科学工程计算研究所
Corresponding AuthorDai YuHong
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Computat Math & Sci Engn Comp, Beijing 100190, Peoples R China
2.Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China
Recommended Citation
GB/T 7714
Dai YuHong,Kou CaiXia. A Barzilai-Borwein conjugate gradient method[J]. SCIENCE CHINA-MATHEMATICS,2016,59(8):1511-1524.
APA Dai YuHong,&Kou CaiXia.(2016).A Barzilai-Borwein conjugate gradient method.SCIENCE CHINA-MATHEMATICS,59(8),1511-1524.
MLA Dai YuHong,et al."A Barzilai-Borwein conjugate gradient method".SCIENCE CHINA-MATHEMATICS 59.8(2016):1511-1524.
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