Volume 28, 2022
|Number of page(s)||36|
|Published online||23 December 2022|
Optimality Conditions and Moreau–Yosida Regularization for Almost Sure State Constraints
2 Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
* Corresponding author: firstname.lastname@example.org
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
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