Optimality conditions and Moreau--Yosida regularization for almost sure state constraints
- Geiersbach, Caroline
- Hintermüller, Michael
2020 Mathematics Subject Classification
- 49K20 49K45 49N15 49J20 90C15
- PDE-constrained optimization under uncertainty, optimization in Banach spaces, optimality conditions, regularization, convex stochastic optimization in Banach spaces, two-stages stochastic optimization, duality
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.