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Multilevel Monte Carlo Finite Element Method for A Stochastic Optimal Control Problem by Sun, Qi; Ming, Ju is a scholarly article available to read on EtoBox.

What is Multilevel Monte Carlo Finite Element Method for A Stochastic Optimal Control Problem about?

In this paper, we consider the implementation of multi-level Monte Carlo method to a stochastic optimal control problem with log-normal coefficients and its surrogate model problem. From the perspective of two optimization problems, i.e., minimizing the accuracy using a fixed computational cost and minimizing the total computational cost to attain a given accuracy, we derive formulas to determine the optimal sample sizes for each level of multi-level Monte Carlo method. Furthermore, we put forward the multi-level Monte Carlo algorithm for our stochastic optimal control problem and some tricks to deal with the multi-level log-normal coefficients. Finally, we present the numerical results of both the elliptic SPDEs and our control problem to validate the effectiveness over the traditional Monte Carlo method.

Author

Sun, Qi; Ming, Ju

Published

2015

Language

EN