Stochastic Two-Stage Programming

1. Front Matter

   Pages i-viii

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2. Preliminaries

   • Karl Frauendorfer

   Pages 1-9

3. Stochastic Two-Stage Problems

   • Karl Frauendorfer

   Pages 11-36

4. Duality and Stability in Convex Optimization (Extended Results for the Saddle Case)

   • Karl Frauendorfer

   Pages 37-65

5. Barycentric Approximation

   • Karl Frauendorfer

   Pages 67-123

6. An Illustrative Survey of Existing Approaches in Stochastic Two-Stage Programming

   • Karl Frauendorfer

   Pages 125-157

7. BRAIN — BaRycentric Approximation for INtegrands (Implementation Issues)

   • Karl Frauendorfer

   Pages 159-184

8. Solving Stochastic Linear Two-Stage Problems (Numerical Results & Computational Experiences)

   • Karl Frauendorfer

   Pages 185-218

9. Back Matter

   Pages 219-232

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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.

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

• Institute for Operations Research, University of Zurich, Zurich, Switzerland

  Karl Frauendorfer

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