AN EFFICIENT GRADIENT PROJECTION METHOD FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS

doi:10.1137/17M1123559

	AN EFFICIENT GRADIENT PROJECTION METHOD FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS
	Gong, Bo 1; Liu, Wenbin 2; Tang, Tao 3; Zhao, Weidong 4,5; Zhou, Tao6
	2017
发表期刊	SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN	0036-1429
卷号	55 期号:6 页码:2982-3005
摘要	In this work, we propose a simple yet effective gradient projection algorithm for a class of stochastic optimal control problems. We first reduce the optimal control problem to an optimization problem for a convex functional by means of a projection operator. Then we propose a convergent iterative scheme for the optimization problem. The key issue in our iterative scheme is to compute the gradient of the objective functional by solving the adjoint equations that are given by backward stochastic differential equations (BSDEs). The Euler method is used to solve the resulting BSDEs. Rigorous convergence analysis is presented, and it is shown that the entire numerical algorithm admits a first order rate of convergence. Several numerical examples are carried out to support the theoretical finding.
关键词	stochastic optimal control gradient projection methods backward stochastic differential equations conditional expectations
DOI	10.1137/17M1123559
语种	英语
资助项目	National Natural Science Foundations of China[91630312] ; National Natural Science Foundations of China[91630203] ; National Natural Science Foundations of China[11571351] ; National Natural Science Foundations of China[11171189] ; National Natural Science Foundations of China[11731006] ; National Natural Science Foundations of China[11571206] ; NCMIS ; Hong Kong Research Grant Council ; Hong Kong Baptist University
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000418663500019
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/29276
专题	计算数学与科学工程计算研究所
通讯作者	Gong, Bo
作者单位	1.Hong Kong Baptist Univ, Dept Math, Hong Kong, Hong Kong, Peoples R China 2.Univ Kent, Kent Business Sch, Canterbury CT2 7PE, Kent, England 3.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China 4.Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China 5.Shandong Univ, Finance Inst, Jinan 250100, Shandong, Peoples R China 6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Gong, Bo,Liu, Wenbin,Tang, Tao,et al. AN EFFICIENT GRADIENT PROJECTION METHOD FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS,2017,55(6):2982-3005.
APA	Gong, Bo,Liu, Wenbin,Tang, Tao,Zhao, Weidong,&Zhou, Tao.(2017).AN EFFICIENT GRADIENT PROJECTION METHOD FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS.SIAM JOURNAL ON NUMERICAL ANALYSIS,55(6),2982-3005.
MLA	Gong, Bo,et al."AN EFFICIENT GRADIENT PROJECTION METHOD FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS".SIAM JOURNAL ON NUMERICAL ANALYSIS 55.6(2017):2982-3005.