KMS Of Academy of mathematics and systems sciences, CAS
| Convergence properties of the BFGS algoritm | |
Dai, YH
| |
| 2003 | |
| Source Publication | SIAM JOURNAL ON OPTIMIZATION
 |
| ISSN | 1052-6234 |
| Volume | 13Issue:3Pages:693-701 |
| Abstract | The BFGS method is one of the most famous quasi-Newton algorithms for unconstrained optimization. In 1984, Powell presented an example of a function of two variables that shows that the Polak-Ribiere-Polyak (PRP) conjugate gradient method and the BFGS quasi-Newton method may cycle around eight nonstationary points if each line search picks a local minimum that provides a reduction in the objective function. In this paper, a new technique of choosing parameters is introduced, and an example with only six cyclic points is provided. It is also noted through the examples that the BFGS method with Wolfe line searches need not converge for nonconvex objective functions. |
| Keyword | unconstrained optimization conjugate gradient method quasi-Newton method Wolfe line search nonconvex global convergence |
| Language | 英语 |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000181475800004 |
| Publisher | SIAM PUBLICATIONS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/18056 |
| 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 Mach & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China |
| Recommended Citation GB/T 7714 | Dai, YH. Convergence properties of the BFGS algoritm[J]. SIAM JOURNAL ON OPTIMIZATION,2003,13(3):693-701. |
| APA | Dai, YH.(2003).Convergence properties of the BFGS algoritm.SIAM JOURNAL ON OPTIMIZATION,13(3),693-701. |
| MLA | Dai, YH."Convergence properties of the BFGS algoritm".SIAM JOURNAL ON OPTIMIZATION 13.3(2003):693-701. |
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