Rates of Convergence in Stochastic Programs with Complete Integer Recourse
Rüdiger Schultz · SIAM Journal on Optimization · 1996
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–Červonenkis 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.