Alternate minimization gradient method

	Alternate minimization gradient method
	Dai, YH; Yuan, YX
	2003-07-01
发表期刊	IMA JOURNAL OF NUMERICAL ANALYSIS
ISSN	0272-4979
卷号	23 期号:3 页码:377-393
摘要	It is well known that the minimization of a smooth function f(x) is equivalent to minimizing its gradient norm parallel tog(x)parallel to(2) in some sense. In this paper, we propose a modified steepest descent method, whose stepsizes alternately minimize the function value and the gradient norm along the line of steepest descent. Hence the name 'alternate minimization (AM) gradient method'. For strictly convex quadratics, the AM method is proved to be Q-superlinearly convergent in two dimensions, and Q-linearly convergent in any dimension. Numerical experiments are presented for symmetric and positive definite linear systems. They suggest that the AM method is much better than the classical steepest descent (SD) method and comparable with some existing gradient methods. They also show that the AM method is an efficient alternative if a solution with a low precision is required. Two variants of the AM method, named shortened SD step gradient methods, are also presented and analysed in this paper. By designing a new kind of line search, the two variants are extended to the field of unconstrained optimization.
关键词	linear system unconstrained optimization gradient method monotonic and nonmonotonic convergence rate line search
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000183834100002
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/18900
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 Math & 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,Yuan, YX. Alternate minimization gradient method[J]. IMA JOURNAL OF NUMERICAL ANALYSIS,2003,23(3):377-393.
APA	Dai, YH,&Yuan, YX.(2003).Alternate minimization gradient method.IMA JOURNAL OF NUMERICAL ANALYSIS,23(3),377-393.
MLA	Dai, YH,et al."Alternate minimization gradient method".IMA JOURNAL OF NUMERICAL ANALYSIS 23.3(2003):377-393.