KMS Of Academy of mathematics and systems sciences, CAS
| Convergence properties of nonlinear conjugate gradient methods | |
Dai, YH; Han, JY; Liu, GH; Sun, DF; Yin, HX; Yuan, YX
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| 2000-02-23 | |
| Source Publication | SIAM JOURNAL ON OPTIMIZATION
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| ISSN | 1052-6234 |
| Volume | 10Issue:2Pages:345-358 |
| Abstract | 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. |
| Keyword | conjugate gradient method descent condition global convergence |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000085671900003 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/15563 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Dai, YH |
| Affiliation | 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 |
| 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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