On Effective Stochastic Galerkin Finite Element Method for Stochastic Optimal Control Governed by Integral-Differential Equations with Random Coefficients (Journal of Computational Mathematics, 2019)
In this paper, we apply stochastic Galerkin finite element methods to the optimalcontrol problem governed by an elliptic integral-differential PDEs with random field. Thecontrol problem has the control constraints of obstacle type. A new gradient algorithmbased on the pre-conditioner conjugate gradient algorithm (PCG) is developed for thisoptimal control problem. This algorithm can transform a part of the state equation matrixand co-state equation matrix into block diagonal matrix and then solve the optimal controlsystems iteratively. The proof of convergence for this algorithm is also discussed. Finallynumerical examples of a medial size are presented to illustrate our theoretical results.