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arXiv · 2206.09160

Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs

Johannes Milz
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Abstract

We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite dimensional control problems. We establish an exponential tail bound for the distance between the finite dimensional problems' solutions and the risk-neutral problem's solution. The tail bound implies that solutions to the risk-neutral optimal control problem can be reliably estimated with the solutions to the finite dimensional control problems. Numerical simulations illustrate our theoretical findings.

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Johannes Milz. 2022-06-18. Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs. https://doi.org/10.1137/22m1503889

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