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.
| ISBN: | 9783540560975 |
| Publication date: | 17th December 1992 |
| Author: | Karl Frauendorfer |
| Publisher: | Springer an imprint of Springer Berlin Heidelberg |
| Format: | Paperback |
| Pagination: | 228 pages |
| Series: | Lecture Notes in Economics and Mathematical Systems |
| Genres: |
Operational research Cybernetics and systems theory Management decision making Optimization Maths for engineers |
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.
Stochastic Two-Stage Programming features in the following genres: Operational research, Cybernetics and systems theory, Management decision making, Optimization, Maths for engineers
Stochastic Two-Stage Programming is available in Paperback
Stochastic Two-Stage Programming was written by Karl Frauendorfer and published by Springer an imprint of Springer Berlin Heidelberg
Stochastic Two-Stage Programming has 228 pages
Yes it is part of Lecture Notes in Economics and Mathematical Systems series