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Convergence properties of nonlinear conjugate gradient methods
Dai, YH; Han, JY; Liu, GH; Sun, DF; Yin, HX; Yuan, YX
2000-02-23
Source PublicationSIAM JOURNAL ON OPTIMIZATION
ISSN1052-6234
Volume10Issue:2Pages:345-358
AbstractRecently, 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.
Keywordconjugate gradient method descent condition global convergence
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000085671900003
PublisherSIAM PUBLICATIONS
Citation statistics
Cited Times:58[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/15563
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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