Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs
arXiv:2206.09160 · doi:10.1137/22M1503889
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.
arXiv comment26 pages, 11 figures
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