Total variation error bounds for convex approximations of two-stage mixed-integer recourse models

Many practical decisions have to be made while future data are uncertain. The stochastic programming approach to such decision problems is to model the uncertain data as random parameters and to assume that all probabilistic information concerning these random parameters is known or can be accurately estimated. A particular class of such models, studied in this thesis, comprises mixed-integer recourse models. These models have a wide range of applications in e.g. engineering, logistics, energy, and finance. They combine the modeling power but also the difficulties of random parameters and integer decision variables, so that in general they are extremely difficult to solve.This thesis contributes to the theory of mixed-integer recourse models by constructing approximations having desirable properties (such as convexity) for optimization purposes. To guarantee the performance of these approximations, error bounds on the approximation error are derived. Several subclasses and problem instances of mixed-integer recourse models are considered, ranging from simple integer recourse models to mixed-integer recourse models in general