Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems

doi:10.1137/S1052623403428683

	Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems
	Hu, QY; Zou, J
	2006
发表期刊	SIAM JOURNAL ON OPTIMIZATION
ISSN	1052-6234
卷号	16 期号:3 页码:798-825
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.
关键词	linear and nonlinear saddle-point problems inexact Uzawa algorithm preconditioning
DOI	10.1137/S1052623403428683
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000235128800008
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2651
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.