Applying the Minimum Risk Criterion in Stochastic Recourse Programs
Computational Optimization and Applications
Quantitative Stability in Stochastic Programming: The Method of Probability Metrics
Mathematics of Operations Research
Mixed-integer value functions in stochastic programming
Combinatorial optimization - Eureka, you shrink!
Stochastic Integer Programming: Limit Theorems and Confidence Intervals
Mathematics of Operations Research
Scenario reduction in stochastic programming with respect to discrepancy distances
Computational Optimization and Applications
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The stability of stochastic programs with mixed-integer recourse and random right-hand sides under perturbations of the integrating probability measure is considered from a quantitative viewpoint. Objective-function values of perturbed stochastic programs are related to each other via a variational distance of probability measures based on a suitable Vapnik--Cervonenkis class of Borel sets in a Euclidean space. This leads to Hölder continuity of local optimal values. In the context of estimation via empirical measures the general results imply qualitative and quantitative statements on the asymptotic convergence of local optimal values and optimal solutions.