Convergence properties of nonlinear conjugate gradient methods

	Convergence properties of nonlinear conjugate gradient methods
	Dai, YH ; Han, JY ; Liu, GH ; Sun, DF ; Yin, HX ; Yuan, YX
	2000-02-23
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	10 期号:2 页码:345-358
摘要	Recently, important contributions on convergence studies of conjugate gradient methods were made by Gilbert and Nocedal [SIAM J. Optim., 2 (1992), pp. 21-42]. They introduce a "sufficient descent condition" to establish global convergence results. Although this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, Gilbert and Nocedal hint that the sufficient descent condition, which was enforced by their two-stage line search algorithm, may be crucial for ensuring the global convergence of conjugate gradient methods. This paper shows that the sufficient descent condition is actually not needed in the convergence analyses of conjugate gradient methods. Consequently, convergence results on the Fletcher-Reeves- and Polak-Ribiere-type methods are established in the absence of the sufficient descent condition. To show the differences between the convergence properties of Fletcher-Reeves- and Polak-Ribiere-type methods, two examples are constructed, showing that neither the boundedness of the level set nor the restriction beta(k) greater than or equal to 0 can be relaxed for the Polak-Ribiere-type methods.
关键词	conjugate gradient method descent condition global convergence
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000085671900003
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/15563
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, Inst Computat Math, LSEC, Beijing 100080, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100080, Peoples R China 3.Northwestern Univ, Dept Ind Engn & Management Sci, Evanston, IL 60208 USA 4.Univ New S Wales, Sch Math, Sydney, NSW 2052, Australia
推荐引用方式 GB/T 7714	Dai, YH,Han, JY,Liu, GH,et al. Convergence properties of nonlinear conjugate gradient methods[J]. SIAM JOURNAL ON OPTIMIZATION,2000,10(2):345-358.
APA	Dai, YH,Han, JY,Liu, GH,Sun, DF,Yin, HX,&Yuan, YX.(2000).Convergence properties of nonlinear conjugate gradient methods.SIAM JOURNAL ON OPTIMIZATION,10(2),345-358.
MLA	Dai, YH,et al."Convergence properties of nonlinear conjugate gradient methods".SIAM JOURNAL ON OPTIMIZATION 10.2(2000):345-358.