Analysis of monotone gradient methods

	Analysis of monotone gradient methods
	Dai, Yu-Hong; Yuan, Ya-xiang
	2005-05-01
发表期刊	JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
ISSN	1547-5816
卷号	1 期号:2 页码:181-192
摘要	The gradient method is one simple method in nonlinear optimization. In this paper, we give a brief review on monotone gradient methods and study their numerical properties by introducing a new technique of long-term observation. We find that, one monotone gradient algorithm which is proposed by Yuan recently shares with the Barzilai-Borwein (BB) method the property that the gradient components with respect to the eigenvectors of the function Hessian are decreasing together. This might partly explain why this algorithm by Yuan is comparable to the BB method in practice. Some examples are also provided showing that the alternate minimization algorithm and the other algorithm by Yuan may fall into cycles. Some more efficient gradient algorithms are provided. Particularly, one of them is monotone and performs better than the BB method in the quadratic case.
关键词	gradient method monotone nonmonotone strictly convex quadratics cycle
语种	英语
WOS研究方向	Engineering ; Operations Research & Management Science ; Mathematics
WOS类目	Engineering, Multidisciplinary ; Operations Research & Management Science ; Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000240847800004
出版者	AMER INST MATHEMATICAL SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1866
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, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Univ Bayreuth, Dept Math, D-95440 Bayreuth, Germany
推荐引用方式 GB/T 7714	Dai, Yu-Hong,Yuan, Ya-xiang. Analysis of monotone gradient methods[J]. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2005,1(2):181-192.
APA	Dai, Yu-Hong,&Yuan, Ya-xiang.(2005).Analysis of monotone gradient methods.JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,1(2),181-192.
MLA	Dai, Yu-Hong,et al."Analysis of monotone gradient methods".JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 1.2(2005):181-192.