Optimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraint

We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vector-valued functions and not only measures. A model problem is given demonstrating the application to PDE-constrained optimization under uncertainty.

Keywords

PDE-constrained optimization under uncertainty, optimization in Banach spaces, optimality conditions, convex stochastic optimization in Banach spaces, two-stage stochastic optimization, regular Lagrange multipliers, duality

URI

https://oa.tib.eu/renate/handle/123456789/9405
https://doi.org/10.34657/8443

Citation

Geiersbach, C., & Wollner, W. (2020). Optimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraint (Vol. 2755). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2755

Collections

Mathematik

License

This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.
Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.

Full item page