KMS Of Academy of mathematics and systems sciences, CAS
On the asymptotic behaviour of some new gradient methods | |
Dai, YH; Fletcher, R | |
2005-07-01 | |
Source Publication | MATHEMATICAL PROGRAMMING |
ISSN | 0025-5610 |
Volume | 103Issue:3Pages:541-559 |
Abstract | The Barzilai-Borwein (BB) gradient method, and some other new gradient methods have shown themselves to be competitive with conjugate gradient methods for solving large dimension nonlinear unconstrained optimization problems. Little is known about the asymptotic behaviour, even when applied to n-dimensional quadratic functions, except in the case that n = 2. We show in the quadratic case how it is possible to compute this asymptotic behaviour, and observe that as n increases there is a transition from superlinear to linear convergence at some value of n >= 4, depending on the method. By neglecting certain terms in the recurrence relations we define simplified versions of the methods, which are able to predict this transition. The simplified methods also predict that for larger values of n, the eigencomponents of the gradient vectors converge in modulus to a common value, which is a similar to a property observed to hold in the real methods. Some unusual and interesting recurrence relations are analysed in the course of the study. |
DOI | 10.1007/s10107-004-0516-9 |
Language | 英语 |
WOS Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
WOS ID | WOS:000229940200006 |
Publisher | SPRINGER |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/1649 |
Collection | 计算数学与科学工程计算研究所 |
Corresponding Author | Dai, YH |
Affiliation | Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China |
Recommended Citation GB/T 7714 | Dai, YH,Fletcher, R. On the asymptotic behaviour of some new gradient methods[J]. MATHEMATICAL PROGRAMMING,2005,103(3):541-559. |
APA | Dai, YH,&Fletcher, R.(2005).On the asymptotic behaviour of some new gradient methods.MATHEMATICAL PROGRAMMING,103(3),541-559. |
MLA | Dai, YH,et al."On the asymptotic behaviour of some new gradient methods".MATHEMATICAL PROGRAMMING 103.3(2005):541-559. |
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