Consistency of sample-based stationary points for infinite-dimensional stochastic optimization

Abstract

We consider stochastic optimization problems with possibly nonsmooth integrands posed in Banach spaces and approximate these stochastic programs via a sample-based approaches. We establish the consistency of approximate Clarke stationary points of the sample-based approximations. Our framework is applied to risk-averse semilinear PDE-constrained optimization using the average value-at-risk and to risk-neutral bilinear PDE-constrained optimization.

20 pages

References in corpus (4)

• Consistency of Monte Carlo Estimators for Risk-Neutral PDE-Constrained Optimization
• Reliable Error Estimates for Optimal Control of Linear Elliptic PDEs with Random Inputs
• Sample Size Estimates for Risk-Neutral Semilinear PDE-Constrained Optimization
• Asymptotic Consistency for Nonconvex Risk-Averse Stochastic Optimization with Infinite Dimensional Decision Spaces