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

Werner Römisch; Thomas M. Surowiec

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arXiv · 2106.06347

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

Werner Römisch·Thomas M. Surowiec

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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.

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BibTeX RIS

Werner Römisch, Thomas M. Surowiec. 2021-06-11. Asymptotic Properties of Monte Carlo Methods in Elliptic PDE-Constrained Optimization under Uncertainty. https://arxiv.org/abs/2106.06347

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