On restart procedures for the conjugate gradient method
文献类型：期刊论文
| 作者 | Dai, YH ; Liao, LZ; Li, D
|
| 刊名 | NUMERICAL ALGORITHMS
 |
| 出版日期 | 2004-04-01 |
| 卷号 | 35期号:2-4页码:249-260 |
| 关键词 | unconstrained optimization conjugate gradient method BFGS updating formula restart global convergence |
| ISSN号 | 1017-1398 |
| 英文摘要 | The conjugate gradient method is a powerful solution scheme for solving unconstrained optimization problems, especially for large-scale problems. However, the convergence rate of the method without restart is only linear. In this paper, we will consider an idea contained in [16] and present a new restart technique for this method. Given an arbitrary descent direction d(t) and the gradient g(t), our key idea is to make use of the BFGS updating formula to provide a symmetric positive definite matrix P-t such that d(t) = - P-t g(t) , and then define the conjugate gradient iteration in the transformed space. Two conjugate gradient algorithms are designed based on the new restart technique. Their global convergence is proved under mild assumptions on the objective function. Numerical experiments are also reported, which show that the two algorithms are comparable to the Beale-Powell restart algorithm. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000220453200008 |
| 出版者 | KLUWER ACADEMIC PUBL |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/19338]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Dai, YH |
| 作者单位 | 1.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China 3.Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Dai, YH,Liao, LZ,Li, D. On restart procedures for the conjugate gradient method[J]. NUMERICAL ALGORITHMS,2004,35(2-4):249-260. |
| APA | Dai, YH,Liao, LZ,&Li, D.(2004).On restart procedures for the conjugate gradient method.NUMERICAL ALGORITHMS,35(2-4),249-260. |
| MLA | Dai, YH,et al."On restart procedures for the conjugate gradient method".NUMERICAL ALGORITHMS 35.2-4(2004):249-260. |
入库方式： OAI收割
来源：数学与系统科学研究院
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