论文标题
风险中性半线性PDE约束优化的样本量估计值
Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization
论文作者
论文摘要
样本平均近似方法（SAA）方法应用于由具有随机输入的半线性椭圆部分微分方程控制的风险中性优化问题。在构建包含SAA临界点的紧凑型集合后，我们使用覆盖号方法来得出SAA临界点的非矩形样本量估计。因此，我们通过SAA临界点获得了获得风险中性PDE限制的优化问题所需的样品数量的上限。我们使用预期和指数尾巴界限来量化准确性。提出了数值插图。
The sample average approximation (SAA) approach is applied to risk-neutral optimization problems governed by semilinear elliptic partial differential equations with random inputs. After constructing a compact set that contains the SAA critical points, we derive nonasymptotic sample size estimates for SAA critical points using the covering number approach. Thereby, we derive upper bounds on the number of samples needed to obtain accurate critical points of the risk-neutral PDE-constrained optimization problem through SAA critical points. We quantify accuracy using expectation and exponential tail bounds. Numerical illustrations are presented.
