The cyclic Barzilai-Borwein method for unconstrained optimization

doi:10.1093/imanum/dr1006

	The cyclic Barzilai-Borwein method for unconstrained optimization
	Dai, Yu-Hong; Hager, William W.; Schittkowski, Klaus ; Zhang, Hongchao
	2006-07-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	26 期号:3 页码:604-627
摘要	In the cyclic Barzilai-Borwein (CBB) method, the same Barzilai-Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 >= 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it is proved that the convergence rate is no better than linear, in general. An implementation of the CBB method, called adaptive cyclic Barzilai-Borwein (ACBB), combines a non-monotone line search and an adaptive choice for the cycle length m. In numerical experiments using the CUTEr test problem library, ACBB performs better than the existing BB gradient algorithm, while it is competitive with the well-known PRP+ conjugate gradient algorithm.
关键词	unconstrained optimization gradient method convex quadratic programming non-monotone line search
DOI	10.1093/imanum/dr1006
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000238907800009
出版者	OXFORD UNIV 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/3873
专题	计算数学与科学工程计算研究所
通讯作者	Dai, Yu-Hong
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100084, Peoples R China 2.Univ Florida, Dept Math, Gainesville, FL 32611 USA 3.Univ Bayreuth, Dept Comp Sci, D-95440 Bayreuth, Germany
推荐引用方式 GB/T 7714	Dai, Yu-Hong,Hager, William W.,Schittkowski, Klaus,et al. The cyclic Barzilai-Borwein method for unconstrained optimization[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2006,26(3):604-627.
APA	Dai, Yu-Hong,Hager, William W.,Schittkowski, Klaus,&Zhang, Hongchao.(2006).The cyclic Barzilai-Borwein method for unconstrained optimization.IMA JOURNAL OF NUMERICAL ANALYSIS,26(3),604-627.
MLA	Dai, Yu-Hong,et al."The cyclic Barzilai-Borwein method for unconstrained optimization".IMA JOURNAL OF NUMERICAL ANALYSIS 26.3(2006):604-627.