Convergence properties of the BFGS algoritm

	Convergence properties of the BFGS algoritm
	Dai, YH
	2003
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	13 期号:3 页码:693-701
摘要	The BFGS method is one of the most famous quasi-Newton algorithms for unconstrained optimization. In 1984, Powell presented an example of a function of two variables that shows that the Polak-Ribiere-Polyak (PRP) conjugate gradient method and the BFGS quasi-Newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the objective function. In this paper, a new technique of choosing parameters is introduced, and an example with only six cyclic points is provided. It is also noted through the examples that the BFGS method with Wolfe line searches need not converge for nonconvex objective functions.
关键词	unconstrained optimization conjugate gradient method quasi-Newton method Wolfe line search nonconvex global convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000181475800004
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18056
专题	计算数学与科学工程计算研究所
通讯作者	Dai, YH
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Mach & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dai, YH. Convergence properties of the BFGS algoritm[J]. SIAM JOURNAL ON OPTIMIZATION,2003,13(3):693-701.
APA	Dai, YH.(2003).Convergence properties of the BFGS algoritm.SIAM JOURNAL ON OPTIMIZATION,13(3),693-701.
MLA	Dai, YH."Convergence properties of the BFGS algoritm".SIAM JOURNAL ON OPTIMIZATION 13.3(2003):693-701.