@Article{IJNAM-19-2-3,
author = {Liuhong, Chen and Xiong, Meixin and Ming, Ju},
title = {Reduced Approach for Stochastic Optimal Control Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2022},
volume = {19},
number = {2-3},
pages = {237--254},
abstract = {<p style="text-align: justify;">In this paper, we develop and analyze the reduced approach for solving optimal
control problems constrained by stochastic partial differential equations (SPDEs). Compared
to the classical approaches based on Monte Carlo method to the solution of stochastic optimal
control and optimization problems, e.g. Lagrange multiplier method, optimization methods based
on sensitivity equations or adjoint equations, our strategy can take best advantage of all sorts of
gradient descent algorithms used to deal with the unconstrained optimization problems but with
less computational cost. Specifically, we represent the sample solutions for the constrained SPDEs
or the state equations by their associated inverse-operators and plug them into the objective
functional to explicitly eliminate the constrains, the constrained optimal control problems are
then converted into the equivalent unconstrained ones, which implies the computational cost for
solving the adjoint equations of the derived Lagrange system is avoided and faster convergent rate
is expected. The stochastic Burgers’ equation with additive white noise is used to illustrate the
performance of our reduced approach. It no doubt has great potential application in stochastic
optimization problems.</p>},
issn = {2617-8710},
doi = {https://doi.org/2022-IJNAM-20479},
url = {https://global-sci.com/article/82933/reduced-approach-for-stochastic-optimal-control-problems}
}