Issue |
ESAIM: COCV
Volume 28, 2022
|
|
---|---|---|
Article Number | 80 | |
Number of page(s) | 36 | |
DOI | https://doi.org/10.1051/cocv/2022070 | |
Published online | 23 December 2022 |
Optimality Conditions and Moreau–Yosida Regularization for Almost Sure State Constraints
1
Weierstrass Institute,
Mohrenstr. 39,
10117
Berlin, Germany
2
Humboldt-Universität zu Berlin,
Unter den Linden 6,
10099
Berlin, Germany
* Corresponding author: caroline.geiersbach@wias-berlin.de
Received:
3
August
2021
Accepted:
28
October
2022
We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable. We obtain strong forms of necessary and sufficient optimality conditions for problems subject to equality and conical constraints. We propose a Moreau-Yosida regularization for the conical constraint and show consistency of the optimality conditions for the regularized problem as the regularization parameter is taken to infinity.
Mathematics Subject Classification: 49K20 / 49K45 / 49N15 / 49J20 / 90C15
Key words: Optimization in Banach spaces / optimality conditions / regularization / convex stochastic optimization in Banach spaces / two-stage stochastic optimization / duality / PDE-constrained optimization under uncertainty
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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