An Efficient Gradient Projection Method for Stochastic Optimal Control Problems

Bo Gong*, Wenbin Liu, Tao Tang, Weidong Zhao, Tao Zhou

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

18 Citations (Scopus)
30 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)2982-3005
Number of pages24
JournalSIAM Journal on Numerical Analysis
Issue number6
Publication statusPublished - 28 Nov 2017

Scopus Subject Areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Backward stochastic differential equations
  • Conditional expectations
  • Gradient projection methods
  • Stochastic optimal control


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