AppliedMath (Feb 2023)

A Multilevel Monte Carlo Approach for a Stochastic Optimal Control Problem Based on the Gradient Projection Method

  • Changlun Ye,
  • Xianbing Luo

DOI
https://doi.org/10.3390/appliedmath3010008
Journal volume & issue
Vol. 3, no. 1
pp. 98 – 116

Abstract

Read online

A multilevel Monte Carlo (MLMC) method is applied to simulate a stochastic optimal problem based on the gradient projection method. In the numerical simulation of the stochastic optimal control problem, the approximation of expected value is involved, and the MLMC method is used to address it. The computational cost of the MLMC method and the convergence analysis of the MLMC gradient projection algorithm are presented. Two numerical examples are carried out to verify the effectiveness of our method.

Keywords