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- ItemOptimality Conditions and Moreau-Yosida Regularization for Almost Sure State Constraints(Paris : EDP Sciences, 2022) 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.
- ItemInterpolation in variable Hilbert scales with application to inverse problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Mathé, Peter; Tautenhahn, UlrichFor solving linear ill-posed problems with noisy data regularization methods are required. In the present paper regularized approximations in Hilbert scales are obtained by a general regularization scheme. The analysis of such schemes is based on new results for interpolation in Hilbert scales. Error bounds are obtained under general smoothness conditions.