Hyung-Chun Lee
Ajou University, Suwon, South Korea

Analysis and Computations of Stochastic Optimal Control Problems
We study mathematically and computationally optimal control problems for stochastic partial differential equations. The control objective is to minimize the expectation of a cost functional, and the control is of the deterministic, boundary value type and/or source term. Mathematically, we prove the existence of an optimal solution and of a Lagrange multiplier; we represent the input data in terms of their Karhunen-Loève expansions and deduce the deterministic optimality system of equations. Computationally, we approximate the finite element solution of the optimality system and estimate its error through the discretizations with respect to both spatial and random parameter spaces. Some numerical experiments are given.