A Barzilai-Borwein conjugate gradient method

doi:10.1007/s11425-016-0279-2

	A Barzilai-Borwein conjugate gradient method
	Dai YuHong1 ; Kou CaiXia 2
	2016-08-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	59 期号:8 页码:1511-1524
摘要	The 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.
关键词	conjugate gradient method subspace minimization Barzilai-Bowein gradient method line search descent property global convergence
DOI	10.1007/s11425-016-0279-2
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000380212100005
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23269
专题	计算数学与科学工程计算研究所
通讯作者	Dai YuHong
作者单位	1.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
推荐引用方式 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.