Inexact Barzilai-Borwein method for saddle point problems
文献类型：期刊论文
| 作者 | Hu, Yi-Qing; Dai, Yu-Hong
|
| 刊名 | NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
 |
| 出版日期 | 2007-05-01 |
| 卷号 | 14期号:4页码:299-317 |
| 关键词 | saddle point problem Uzawa algorithm Barzilai-Borwein method R-linear convergence |
| ISSN号 | 1070-5325 |
| DOI | 10.1002/nla.516 |
| 英文摘要 | This paper considers the inexact Barzilai-Borwein (BB) algorithm applied to saddle point problems. To this aim, we study the convergence properties of the inexact BB algorithm for symmetric positive definite linear systems. Suppose that g(k) and (g) over tilde (k) are the exact residual and its approximation of the linear system at the k th iteration, respectively. We prove the R-linear convergence of the algorithm if vertical bar vertical bar(g) over tilde (k) - g(k) vertical bar vertical bar <= eta vertical bar vertical bar (g) over tilde (k) vertical bar vertical bar for some small eta>0 and all k. To adapt the algorithm for solving saddle point problems, we also extend the R-linear convergence result to the case when the right-hand term vertical bar vertical bar (g) over tilde (k) vertical bar vertical bar is replaced by vertical bar vertical bar (g) over tilde (k-1) vertical bar vertical bar. Although our theoretical analyses cannot provide a good estimate to the parameter eta, in practice, we find that eta can he as large as the one in the inexact Uzawa algorithm. Further numerical experiments show that the inexact BB algorithm performs well for the tested saddle point problems. Copyright (c) 2007 John Wiley & Sons, Ltd. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000245958400004 |
| 出版者 | JOHN WILEY & SONS LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/5146]  |
| 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 | 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 | Hu, Yi-Qing,Dai, Yu-Hong. Inexact Barzilai-Borwein method for saddle point problems[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2007,14(4):299-317. |
| APA | Hu, Yi-Qing,&Dai, Yu-Hong.(2007).Inexact Barzilai-Borwein method for saddle point problems.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,14(4),299-317. |
| MLA | Hu, Yi-Qing,et al."Inexact Barzilai-Borwein method for saddle point problems".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 14.4(2007):299-317. |
入库方式： OAI收割
来源：数学与系统科学研究院
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