Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems
文献类型：期刊论文
| 作者 | Hu, QY ; Zou, J
|
| 刊名 | SIAM JOURNAL ON OPTIMIZATION
 |
| 出版日期 | 2006 |
| 卷号 | 16期号:3页码:798-825 |
| 关键词 | linear and nonlinear saddle-point problems inexact Uzawa algorithm preconditioning |
| ISSN号 | 1052-6234 |
| DOI | 10.1137/S1052623403428683 |
| 英文摘要 | This paper proposes some nonlinear Uzawa methods for solving linear and nonlinear saddle-point problems. A nonlinear inexact Uzawa algorithm is first introduced for linear saddle-point problems. Two different PCG techniques are allowed in the inner and outer iterations of the algorithm. This algorithm is then extended for a class of nonlinear saddle-point problems arising from some convex optimization problems with linear constraints. For this extension, some PCG method used in the inner iteration needs to be carefully constructed so that it converges in a certain energy norm instead of the usual l(2)-norm. It is shown that the new algorithm converges under some practical conditions and there is no need for any a priori estimates on the minimal and maximal eigenvalues of the two local preconditioned systems involved. The two new methods perform more efficiently than the existing methods in the cases where no good preconditioners are available for the Schur complements. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000235128800008 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/2650]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Hu, QY |
| 作者单位 | 1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Hu, QY,Zou, J. Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems[J]. SIAM JOURNAL ON OPTIMIZATION,2006,16(3):798-825. |
| APA | Hu, QY,&Zou, J.(2006).Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems.SIAM JOURNAL ON OPTIMIZATION,16(3),798-825. |
| MLA | Hu, QY,et al."Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems".SIAM JOURNAL ON OPTIMIZATION 16.3(2006):798-825. |
入库方式： OAI收割
来源：数学与系统科学研究院
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