Stochastic Two-Stage Programming

Stochastic programming offers models and methods for decision problems where some of the data are uncertain. These models have features and structural properties which are preferably exploited by SP methods within the solution process. This work contributes to the methodology for two-stage models. In these models, the objective function is given as an integral, whose integrand depends on a random vector, on its probability measure and on a decision. The main results of this work are as follows: after investigating duality relations for convex optimization problems with supply/demand and prices treated as parameters, a stability criterion is stated and proves subdifferentiability of the value function. This criterion is employed for proving the existence of bilinear functions which minorize/majorize the integrand. Additionally, these minorants/majorants support the integrand on generalized barycentres of simplicial faces of specially shaped polytopes and amount to an approach called the barycentric approximation scheme.