On restart procedures for the conjugate gradient method

	On restart procedures for the conjugate gradient method
	Dai, YH; Liao, LZ ; Li, D
	2004-04-01
发表期刊	NUMERICAL ALGORITHMS
ISSN	1017-1398
卷号	35 期号:2-4 页码:249-260
摘要	The conjugate gradient method is a powerful solution scheme for solving unconstrained optimization problems, especially for large-scale problems. However, the convergence rate of the method without restart is only linear. In this paper, we will consider an idea contained in [16] and present a new restart technique for this method. Given an arbitrary descent direction d(t) and the gradient g(t), our key idea is to make use of the BFGS updating formula to provide a symmetric positive definite matrix P-t such that d(t) = - P-t g(t) , and then define the conjugate gradient iteration in the transformed space. Two conjugate gradient algorithms are designed based on the new restart technique. Their global convergence is proved under mild assumptions on the objective function. Numerical experiments are also reported, which show that the two algorithms are comparable to the Beale-Powell restart algorithm.
关键词	unconstrained optimization conjugate gradient method BFGS updating formula restart global convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000220453200008
出版者	KLUWER ACADEMIC PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/19339
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	1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China 3.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Dai, YH,Liao, LZ,Li, D. On restart procedures for the conjugate gradient method[J]. NUMERICAL ALGORITHMS,2004,35(2-4):249-260.
APA	Dai, YH,Liao, LZ,&Li, D.(2004).On restart procedures for the conjugate gradient method.NUMERICAL ALGORITHMS,35(2-4),249-260.
MLA	Dai, YH,et al."On restart procedures for the conjugate gradient method".NUMERICAL ALGORITHMS 35.2-4(2004):249-260.