Stochastic Two-Stage Programming

Karl Frauendorfer

ISBN 10: 3540560971 / ISBN 13: 9783540560975

Published by Springer Berlin Heidelberg, 1992

About this Item

Druck auf Anfrage Neuware - Printed after ordering - Stochastic Programming offers models and methods fordecision problems wheresome of the data are uncertain.These models have features and structural properties whichare preferably exploited by SP methods within the solutionprocess. This work contributes to the methodology fortwo-stagemodels. In these models the objective function isgiven as an integral, whose integrand depends on a randomvector, on its probability measure and on a decision.The main results of this work have been derived with theintention to ease these difficulties: After investigatingduality relations for convex optimization problems withsupply/demand and prices being treated as parameters, astability criterion is stated and provessubdifferentiability of the value function. This criterionis employed for proving the existence of bilinear functions,which minorize/majorize the integrand. Additionally, theseminorants/majorants support the integrand on generalizedbarycenters of simplicial faces of specially shapedpolytopes and amount to an approach which is denotedbarycentric approximation scheme.

Seller Inventory # 9783540560975

Bibliographic Details

• Title: Stochastic Two-Stage Programming
• Publisher: Springer Berlin Heidelberg
• Publication Date: 1992
• Language: English
• ISBN 10: 3540560971
• ISBN 13: 9783540560975
• Binding: Taschenbuch
• Condition: Neu

About this title

Synopsis

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.