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

2021/06/11 by Römisch, Werner, Surowiec, Thomas M. · 1 citation
#49J20 49J55 60F17 65C05 90C15 35R60 #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2106.06347

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^-(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.

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