A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

	A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM
	Liu, Wenbin 1,2; Gong, Wei3 ; Yan, Ningning3
	2009
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	27 期号:1 页码:97-114
摘要	In this paper, we study numerical methods for an optimal control problem with point-wise state constraints. The traditional approaches often need to deal with the delta-singularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation, In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms (non conforming finite element approximation) are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.
关键词	Optimal control problem State-constraints Fourth order variational inequalities Nonconforming finite element method
语种	英语
资助项目	National Natural Science Foundation of China[60474027] ; National Natural Science Foundation of China[10771211] ; National Basic Research Program[2005CB321701]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000263626900005
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7140
专题	计算数学与科学工程计算研究所系统科学研究所
通讯作者	Liu, Wenbin
作者单位	1.Univ Kent, KBS, Canterbury CT2 7NF, Kent, England 2.Univ Kent, Inst Math & Stat, Canterbury CT2 7NF, Kent, England 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Liu, Wenbin,Gong, Wei,Yan, Ningning. A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2009,27(1):97-114.
APA	Liu, Wenbin,Gong, Wei,&Yan, Ningning.(2009).A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM.JOURNAL OF COMPUTATIONAL MATHEMATICS,27(1),97-114.
MLA	Liu, Wenbin,et al."A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM".JOURNAL OF COMPUTATIONAL MATHEMATICS 27.1(2009):97-114.