A new stepsize for the steepest descent method
文献类型：期刊论文
| 作者 | Yuan, YX
|
| 刊名 | JOURNAL OF COMPUTATIONAL MATHEMATICS
 |
| 出版日期 | 2006-03-01 |
| 卷号 | 24期号:2页码:149-156 |
| 关键词 | steepest descent line search unconstrained optimization convergence |
| ISSN号 | 0254-9409 |
| 英文摘要 | The steepest descent method is the simplest gradient method for optimization. It is well known that exact line searches along each steepest descent direction may converge very slowly. An important result was given by Barzilar and Borwein, which is proved to be superlinearly convergent for convex quadratic in two dimensional space, and performs quite well for high dimensional problems. The BB method is not monotone, thus it is not easy to be generalized for general nonlinear functions unless certain non-monotone techniques being applied. Therefore, it is very desirable to find stepsize formulae which enable fast convergence and possess the monotone property. Such a stepsize alpha(k) for the steepest descent method is suggested in this paper. An algorithm with this new stepsize in even iterations and exact line search in odd iterations is proposed. Numerical results are presented, which confirm that the new method can find the exact solution within 3 iteration for two dimensional problems. The new method is very efficient for small scale problems. A modified version of the new method is also presented, where the new technique for selecting the stepsize is used after every two exact line searches. The modified algorithm is comparable to the Barzilar-Borwein method for large scale problems and better for small scale problems. |
| 语种 | 英语 |
| WOS记录号 | WOS:000235901100004 |
| 出版者 | VSP BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/2928]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Yuan, YX |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, LSEC ICMSEC, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Yuan, YX. A new stepsize for the steepest descent method[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2006,24(2):149-156. |
| APA | Yuan, YX.(2006).A new stepsize for the steepest descent method.JOURNAL OF COMPUTATIONAL MATHEMATICS,24(2),149-156. |
| MLA | Yuan, YX."A new stepsize for the steepest descent method".JOURNAL OF COMPUTATIONAL MATHEMATICS 24.2(2006):149-156. |
入库方式： OAI收割
来源：数学与系统科学研究院
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