@article{43a8c2ef06d64869831a0ec1137f793a,
title = "An efficient gradient projection method for stochastic optimal control problems",
abstract = "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.",
keywords = "Backward stochastic differential equations, Conditional expectations, Gradient projection methods, Stochastic optimal control",
author = "Bo Gong and Wenbin Liu and Tao TANG and Weidong Zhao and Tao Zhou",
note = "Funding Information: ∗Received by the editors March 30, 2017; accepted for publication (in revised form) September 1, 2017; published electronically November 28, 2017. http://www.siam.org/journals/sinum/55-6/M112355.html Funding: This work was supported by the National Natural Science Foundations of China under grants 91630312, 91630203, 11571351, 11171189, 11731006, and 11571206. The last author is also supported by NCMIS. The third and first authors are supported by the Hong Kong Research Grant Council and Hong Kong Baptist University. †Department of Mathematics, The Hong Kong Baptist University, Hong Kong, China (13479245@ life.hkbu.edu.hk). ‡Kent Business School, University of Kent, Canterbury CT2 7PE, UK (W.B.Liu@kent.ac.uk). §Department of Mathematics, Southern University of Sciences and Technology, Shenzhen, Guangdong 518055, China (tangt@sustc.edu.cn). ¶School of Mathematics & Finance Institute, Shandong University, Jinan, Shandong 250100, China (wdzhao@sdu.edu.cn). ‖LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China (tzhou@lsec.cc.ac.cn).",
year = "2017",
doi = "10.1137/17M1123559",
language = "English",
volume = "55",
pages = "2982--3005",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "6",
}