Stochastic Programming offers models and methods for decision
problems wheresome 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-stagemodels. 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 have been derived with the intention to
ease these difficulties: After investigating duality relations for
convex optimization problems with supply/demand and prices being
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
barycenters of simplicial faces of specially shaped polytopes and
amount to an approach which is denoted barycentric approximation
scheme.
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