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.
翻译:正在研究随机线性椭圆形PDE限制优化问题的蒙特卡洛近似值。 我们使用实验过程理论来获取最佳价值和解决方案的最佳平均趋同率$(n ⁇ -\frac{1 ⁇ 2 ⁇ ),以及最佳价值的核心限制理论。 后者允许使用重新标本技术确定零星一致的置信间隔。