Alternate step gradient method

doi:10.1080/02331930310001611547

CSpace

	Alternate step gradient method
	Dai, YH
	2003-08-01
发表期刊	OPTIMIZATION
ISSN	0233-1934
卷号	52 期号:4-5 页码:395-415
摘要	The Barzilai and Borwein (BB) gradient method does not guarantee a descent in the objective function at each iteration, but performs better than the classical steepest descent (SD) method in practice. So far, the BB method has found many successful applications and generalizations in linear systems. unconstrained optimization, convex-constrained optimization, stochastic optimization, etc. In this article. we propose a new gradient method that uses the SD and the 1313 steps alternately. Hence the name "alternate step (AS) gradient method." Our theoretical and numerical analyses show that the AS method is a promising alternative to the 1313 method for linear systems. Unconstrained optimization algorithms related to the AS method are also discussed. particularly, a more efficient gradient algorithm is provided by exploring the idea of the AS method in the GBB algorithm by Raydan (1997). To establish a general R-linear convergence result for gradient methods, an important property of the stepsize is drawn in this article. Consequently, R-linear convergence result is established for a large collection of gradient methods, including the AS method. Some interesting insights into gradient methods and discussion about monotonicity and nonmonotonicity are also given.
关键词	linear system unconstrained optimizations gradient method convergence rate nonmonotone line search
DOI	10.1080/02331930310001611547
语种	英语
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000186897600003
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18738
专题	中国科学院数学与系统科学研究院
通讯作者	Dai, YH
作者单位	Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Dai, YH. Alternate step gradient method[J]. OPTIMIZATION,2003,52(4-5):395-415.
APA	Dai, YH.(2003).Alternate step gradient method.OPTIMIZATION,52(4-5),395-415.
MLA	Dai, YH."Alternate step gradient method".OPTIMIZATION 52.4-5(2003):395-415.