Year: 2021
Communications in Mathematical Research , Vol. 37 (2021), Iss. 3 : pp. 387–420
Abstract
In this work, we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation approach to implement spatial dimension approximation. Our main contribution is to extend the existing gradient projection method to moderate high-dimensional space. The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework, and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach. We also present several numerical experiments to validate the theoretical results of our approach and demonstrate the performance meshfree approximation in solving stochastic optimal control problems.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2021-0022
Communications in Mathematical Research , Vol. 37 (2021), Iss. 3 : pp. 387–420
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Stochastic optimal control maximum principle backward stochastic differential equations meshfree approximation.
Author Details
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A PDE-BASED ADAPTIVE KERNEL METHOD FOR SOLVING OPTIMAL FILTERING PROBLEMS
Zhang, Zezhong
Archibald, Richard
Bao, Feng
Journal of Machine Learning for Modeling and Computing, Vol. 3 (2022), Iss. 3 P.37
https://doi.org/10.1615/JMachLearnModelComput.2022043526 [Citations: 0]