"Optimality conditions and approximation in infinite-dimensional stochastic optimization"Geiersbach, CarolineThis talk is concerned with a class of risk-neutral stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. These problems have applications in physics-based models where a system described by a partial differential equation (PDE) with random inputs or parameters should be optimized, and where additional constraints on the PDE's solution are imposed. For this class of problems, we investigate the consistency of optimal values and solutions corresponding to sample average approximation (SAA) as the sample size is taken to infinity. Additionally, the consistency of SAA Karush--Kuhn--Tucker conditions with Moreau--Yosida-type regularization is shown under mild conditions. This work provides theoretical justification for the numerical computation of solutions frequently used in the literature and in experimentation. Examples from PDE-constrained optimization under uncertainty are analyzed, demonstrating how the framework can be used in practice. Joint work with: Johannes Milz |
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