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

Johannes Milz

doi:10.1137/23m1600608

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arXiv · 2306.17032

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

Johannes Milz

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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.

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Johannes Milz. 2023-06-29. Consistency of sample-based stationary points for infinite-dimensional stochastic optimization. https://doi.org/10.1137/23m1600608

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