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- ItemOptimality conditions for convex stochastic optimization problems in Banach spaces with almost sure state constraint(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Geiersbach, Caroline; Wollner, WinnifriedWe 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.
- ItemOptimality conditions and Moreau--Yosida regularization for almost sure state constraints(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Geiersbach, Caroline; Hintermüller, MichaelWe 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.