Multigrid Methods and Sparse-Grid Collocation Techniques for Parabolic Optimal Control Problems with Random Coefficients

An efficient computational framework to solve nonlinear parabolic optimal control problems with random coefficients is presented. This framework allows us to investigate the influence of randomness or uncertainty of problem's parameters values on the control provided by the optimal control theory. The proposed framework combines space-time multigrid methods with sparse-grid collocation techniques. Theoretical and numerical results of computation of stochastic optimal control solutions and formulation of mean control functions are presented.