Alternate step gradient method
文献类型：期刊论文
| 作者 | Dai, YH |
| 刊名 | OPTIMIZATION
 |
| 出版日期 | 2003-08-01 |
| 卷号 | 52期号:4-5页码:395-415 |
| 关键词 | linear system unconstrained optimizations gradient method convergence rate nonmonotone line search |
| ISSN号 | 0233-1934 |
| DOI | 10.1080/02331930310001611547 |
| 英文摘要 | The Barzilai and Borwein (BB) gradient method does not guarantee a descent in the objective function at each iteration, but performs better than the classical steepest descent (SD) method in practice. So far, the BB method has found many successful applications and generalizations in linear systems. unconstrained optimization, convex-constrained optimization, stochastic optimization, etc. In this article. we propose a new gradient method that uses the SD and the 1313 steps alternately. Hence the name "alternate step (AS) gradient method." Our theoretical and numerical analyses show that the AS method is a promising alternative to the 1313 method for linear systems. Unconstrained optimization algorithms related to the AS method are also discussed. particularly, a more efficient gradient algorithm is provided by exploring the idea of the AS method in the GBB algorithm by Raydan (1997). To establish a general R-linear convergence result for gradient methods, an important property of the stepsize is drawn in this article. Consequently, R-linear convergence result is established for a large collection of gradient methods, including the AS method. Some interesting insights into gradient methods and discussion about monotonicity and nonmonotonicity are also given. |
| 语种 | 英语 |
| WOS记录号 | WOS:000186897600003 |
| 出版者 | TAYLOR & FRANCIS LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/18737]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Dai, YH |
| 作者单位 | Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Dai, YH. Alternate step gradient method[J]. OPTIMIZATION,2003,52(4-5):395-415. |
| APA | Dai, YH.(2003).Alternate step gradient method.OPTIMIZATION,52(4-5),395-415. |
| MLA | Dai, YH."Alternate step gradient method".OPTIMIZATION 52.4-5(2003):395-415. |
入库方式： OAI收割
来源：数学与系统科学研究院
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