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Stochastic Two-Stage Programming

  • Karl Frauendorfer

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 392)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Karl Frauendorfer
    Pages 1-9
  3. Karl Frauendorfer
    Pages 11-36
  4. Karl Frauendorfer
    Pages 67-123
  5. Back Matter
    Pages 219-232

About this book

Introduction

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.

Keywords

Decision Theory Stochastic Programming mathematical programming mathematische Programmierung optimization probability measure programming stochastische Entscheidungstheorie stochastische Programmierung

Authors and affiliations

  • Karl Frauendorfer
    • 1
  1. 1.Institute for Operations ResearchUniversity of ZurichZurichSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-95696-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 1992
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56097-5
  • Online ISBN 978-3-642-95696-6
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site