论文标题
可靠的误差估计值，用于对随机输入的线性椭圆PDE的最佳控制
Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs
论文作者
论文摘要
我们将使用基于蒙特卡洛样本的近似值和有限的元素离散化的线性椭圆偏微分方程和有限的元素离散化，从而使风险中和最佳控制问题离散，并带有随机输入。我们为有限维问题解决方案与风险中立问题解决方案之间的距离建立了指数式尾巴。尾巴结合意味着可以通过有限维控制问题的解决方案可靠地估计了风险中性最佳控制问题的解决方案。数值模拟说明了我们的理论发现。
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.
