南方科技大学知识苑(SUSTech KC): EFFICIENT NUMERICAL METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENT

题名	EFFICIENT NUMERICAL METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENT
作者	Pang, Xiaowei 1; Song, Haiming 1; Wang, Xiaoshen 2; Zhang, Jiachuan3,4
通讯作者	Song, Haiming
发表日期	2020-06
DOI	10.3934/era.2020053
发表期刊	Electronic Research Archive 影响因子和分区
ISSN	2688-1594
EISSN	2688-1594
卷号	28 期号:2页码:1001-1022
摘要	Efficient numerical methods for solving Poisson equation constraint optimal control problems with random coefficient are discussed in this paper. By applying the finite element method and the Monte Carlo approximation, the original optimal control problem is discretized and transformed into an optimization problem. Taking advantage of the separable structures, Algorithm 1 is proposed for solving the problem, where an alternating direction method of multiplier is used. Both computational and storage costs of this algorithm are very high. In order to reduce the computational cost, Algorithm 2 is proposed, where the multi-modes expansion is introduced and applied. Further, for reducing the storage cost, we propose Algorithm 3 based on Algorithm 2. The main idea is that the random term is shifted to the objective functional, which could be computed in advance. Therefore, we only need to solve a deterministic optimization problem, which could reduce all the costs significantly. Moreover, the convergence analyses of the proposed algorithms are established, and numerical simulations are carried out to test the performances of them.
关键词	Optimal control problem finite element method Monte Carlo approximation alternating direction method of multiplier multi-modes expansion
相关链接	[来源记录]
收录类别	SCI
语种	英语
学校署名	其他
资助项目	NSF of China[11701210][11871245][11771179][11726102][11971221][11731006] ; science and technology department project of Jilin Province[20190103029JH][20200201269JC] ; education department project of Jilin Province[JJKH20180113KJ] ; Shenzhen Sci-Tech Fund[JCYJ20170818153840322][JCYJ20190809150413261] ; Guangdong Provincial Key Laboratory of Computational Science and Material Design[2019B030301001]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000544123800024
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
来源库	Web of Science
引用统计	被引频次[WOS]：1
成果类型	期刊论文
条目标识符	http://sustech.caswiz.com/handle/2SGJ60CL/141496
专题	理学院_数学系工学院_材料科学与工程系
作者单位	1.Jilin Univ, Sch Math, Changchun 130012, Peoples R China 2.Univ Arkansas, Dept Math & Stat, Little Rock, AR 72204 USA 3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China 4.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China
推荐引用方式 GB/T 7714	Pang, Xiaowei,Song, Haiming,Wang, Xiaoshen,et al. EFFICIENT NUMERICAL METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENT[J]. Electronic Research Archive,2020,28(2):1001-1022.
APA	Pang, Xiaowei,Song, Haiming,Wang, Xiaoshen,&Zhang, Jiachuan.(2020).EFFICIENT NUMERICAL METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENT.Electronic Research Archive,28(2),1001-1022.
MLA	Pang, Xiaowei,et al."EFFICIENT NUMERICAL METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH RANDOM COEFFICIENT".Electronic Research Archive 28.2(2020):1001-1022.