Analysis of monotone gradient methods
文献类型：期刊论文
| 作者 | Dai, Yu-Hong ; Yuan, Ya-xiang
|
| 刊名 | JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
 |
| 出版日期 | 2005-05-01 |
| 卷号 | 1期号:2页码:181-192 |
| 关键词 | gradient method monotone nonmonotone strictly convex quadratics cycle |
| ISSN号 | 1547-5816 |
| 英文摘要 | The gradient method is one simple method in nonlinear optimization. In this paper, we give a brief review on monotone gradient methods and study their numerical properties by introducing a new technique of long-term observation. We find that, one monotone gradient algorithm which is proposed by Yuan recently shares with the Barzilai-Borwein (BB) method the property that the gradient components with respect to the eigenvectors of the function Hessian are decreasing together. This might partly explain why this algorithm by Yuan is comparable to the BB method in practice. Some examples are also provided showing that the alternate minimization algorithm and the other algorithm by Yuan may fall into cycles. Some more efficient gradient algorithms are provided. Particularly, one of them is monotone and performs better than the BB method in the quadratic case. |
| WOS研究方向 | Engineering ; Operations Research & Management Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000240847800004 |
| 出版者 | AMER INST MATHEMATICAL SCIENCES |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/1865]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Dai, Yu-Hong |
| 作者单位 | 1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, State Key Lab Sci & Engn Comp, Beijing 100080, Peoples R China 2.Univ Bayreuth, Dept Math, D-95440 Bayreuth, Germany |
| 推荐引用方式 GB/T 7714 | Dai, Yu-Hong,Yuan, Ya-xiang. Analysis of monotone gradient methods[J]. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,2005,1(2):181-192. |
| APA | Dai, Yu-Hong,&Yuan, Ya-xiang.(2005).Analysis of monotone gradient methods.JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION,1(2),181-192. |
| MLA | Dai, Yu-Hong,et al."Analysis of monotone gradient methods".JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 1.2(2005):181-192. |
入库方式： OAI收割
来源：数学与系统科学研究院
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