论文标题
蒙特卡洛估计量的一致性，对风险中性PDE受限优化
Consistency of Monte Carlo Estimators for Risk-Neutral PDE-Constrained Optimization
论文作者
论文摘要
我们将样本平均值（SAA）方法应用于由随机输入的非线性部分微分方程（PDE）控制的风险中性优化问题。我们分析了SAA最佳值和SAA解决方案的一致性。我们的分析利用了PDE受限的优化问题中的问题结构，使我们能够构建可行集合的确定性，紧凑的子集，该集合包含有关风险中性问题的解决方案，最终包含SAA问题的解决方案。该构建用于使用有关随机编程的文献中建立的结果来研究一致性。我们的框架的假设在不确定性下的三个非线性优化问题上进行了验证。
We apply the sample average approximation (SAA) method to risk-neutral optimization problems governed by nonlinear partial differential equations (PDEs) with random inputs. We analyze the consistency of the SAA optimal values and SAA solutions. Our analysis exploits problem structure in PDE-constrained optimization problems, allowing us to construct deterministic, compact subsets of the feasible set that contain the solutions to the risk-neutral problem and eventually those to the SAA problems. The construction is used to study the consistency using results established in the literature on stochastic programming. The assumptions of our framework are verified on three nonlinear optimization problems under uncertainty.
