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

arXiv: https://arxiv.org/abs/2306.17032 · HTML: https://mlsanity.com/paper/2306.17032/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Failure of uniform laws of large numbers for subdifferentials and beyond](https://mlsanity.com/paper/2511.16568/) (2025)
- [Lipschitzian SLLNs for random functions](https://mlsanity.com/paper/2607.20411/) (2026)

## Abstract (arXiv)

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.