Asymptotic Properties of Monte Carlo Methods in Elliptic PDE-Constrained Optimization under Uncertainty

Abstract

Monte Carlo approximations for random linear elliptic PDE constrained optimization problems are studied. We use empirical process theory to obtain best possible mean convergence rates $O(n^{-\frac{1}{2}})$ for optimal values and solutions, and a central limit theorem for optimal values. The latter allows to determine asymptotically consistent confidence intervals by using resampling techniques.