A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION

doi:10.4208/jcm.1706-m2016-0721

	A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION
	Chen, Chong1,2 ; Wen, Zaiwen 3; Yuan, Yaxiang2
	2018
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	36 期号:6 页码:881-902
摘要	A new two-level subspace method is proposed for solving the general unconstrained minimization formulations discretized from infinite-dimensional optimization problems. At each iteration, the algorithm executes either a direct step on the current level or a coarse subspace correction step. In the coarse subspace correction step, we augment the traditional coarse grid space by a two-dimensional subspace spanned by the coordinate direction and the gradient direction at the current point. Global convergence is proved and convergence rate is studied under some mild conditions on the discretized functions. Preliminary numerical experiments on a few variational problems show that our two-level subspace method is promising.
关键词	Nonlinear optimization Convex and nonconvex problems Subspace technique Multigrid/multilevel method Large-scale problems
DOI	10.4208/jcm.1706-m2016-0721
语种	英语
资助项目	NSFC[11331012] ; NSFC[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000455997200007
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32238
专题	计算数学与科学工程计算研究所
通讯作者	Chen, Chong
作者单位	1.Univ Chinese Acad Sci, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 3.Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China
推荐引用方式 GB/T 7714	Chen, Chong,Wen, Zaiwen,Yuan, Yaxiang. A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2018,36(6):881-902.
APA	Chen, Chong,Wen, Zaiwen,&Yuan, Yaxiang.(2018).A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION.JOURNAL OF COMPUTATIONAL MATHEMATICS,36(6),881-902.
MLA	Chen, Chong,et al."A GENERAL TWO-LEVEL SUBSPACE METHOD FOR NONLINEAR OPTIMIZATION".JOURNAL OF COMPUTATIONAL MATHEMATICS 36.6(2018):881-902.