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An Efficient Gradient Projection Method for Stochastic Optimal Control Problems

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). pp. 2982-3005. ISSN 0036-1429. (doi:10.1137/17M1123559)

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https://doi.org/10.1137/17M1123559

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.

Item Type: Article
DOI/Identification number: 10.1137/17M1123559
Divisions: Faculties > Social Sciences > Kent Business School
Depositing User: Steve Wenbin Liu
Date Deposited: 19 Dec 2017 10:41 UTC
Last Modified: 29 May 2019 20:08 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/65556 (The current URI for this page, for reference purposes)
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