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arXiv · 2108.01391

Optimality Conditions and Moreau--Yosida Regularization for Almost Sure State Constraints

Caroline Geiersbach·Michael Hintermüller
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Abstract

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.

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Caroline Geiersbach, Michael Hintermüller. 2021-08-03. Optimality Conditions and Moreau--Yosida Regularization for Almost Sure State Constraints. https://arxiv.org/abs/2108.01391

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