Asymptotic Properties of Monte Carlo Methods in Elliptic PDE-Constrained Optimization under Uncertainty
Optimization and Control
2021-06-14 v1 Numerical Analysis
Numerical Analysis
Probability
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 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.
Keywords
Cite
@article{arxiv.2106.06347,
title = {Asymptotic Properties of Monte Carlo Methods in Elliptic PDE-Constrained Optimization under Uncertainty},
author = {Werner Römisch and Thomas M. Surowiec},
journal= {arXiv preprint arXiv:2106.06347},
year = {2021}
}