Stochastic Two-Stage Programming (Paperback)

Karl Frauendorfer

ISBN 10: 3540560971 / ISBN 13: 9783540560975

Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 1992

Paperback. 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. Stochastic Programming offers models and methods fordecision problems wheresome of the data are uncertain. In these models the objective function isgiven as an integral, whose integrand depends on a randomvector, on its probability measure and on a decision. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Bestandsnummer des Verkäufers 9783540560975

Inhaltsangabe:

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.

Reseña del editor: 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.

Bibliografische Details

Titel: Stochastic Two-Stage Programming (Paperback)
Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
Erscheinungsdatum: 1992
Einband: Paperback
Zustand: new