Abstract
We consider an optimal control problem governed by an elliptic partial differential equation (PDE) with random coefficient, and introduce an efficient numerical method for the problem under concern. Based on a finite element discretization of the constraint PDE and objective functional, an ADAM-type iteration scheme is proposed to compute the approximated optimal control, which equips the stochastic gradient iteration with modified momentum acceleration and adaptive step size. We provide theoretical bounds on both the discretization and iteration error of the proposed numerical method. Our method is tested on two examples, and the numerical results show the efficiency and performance of the method.
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