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AN EFFICIENT GRADIENT PROJECTION METHOD FOR STOCHASTIC OPTIMAL CONTROL PROBLEMS
Gong, Bo1; Liu, Wenbin2; Tang, Tao3; Zhao, Weidong4,5; Zhou, Tao6
2017
Source PublicationSIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN0036-1429
Volume55Issue:6Pages:2982-3005
AbstractIn 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.
Keywordstochastic optimal control gradient projection methods backward stochastic differential equations conditional expectations
DOI10.1137/17M1123559
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000418663500019
PublisherSIAM PUBLICATIONS
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29276
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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