Generalized Bounds for Convex Multistage Stochastic Programs

Generalized Bounds for Convex Multistage Stochastic Programs

by Daniel Kuhn
     
 

This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or their extensions are generally not available for such problems, tight bounds can systematically be constructed under mild

Overview

This book investigates convex multistage stochastic programs whose objective and constraint functions exhibit a generalized nonconvex dependence on the random parameters. Although the classical Jensen and Edmundson-Madansky type bounds or their extensions are generally not available for such problems, tight bounds can systematically be constructed under mild regularity conditions. A distinct primal-dual symmetry property is revealed when the proposed bounding method is applied to linear stochastic programs. Exemplary applications are studied to assess the performance of the theoretical concepts in situations of practical relevance. It is shown how market power, lognormal stochastic processes, and risk-aversion can be properly handled in a stochastic programming framework. Numerical experiments show that the relative gap between the bounds can typically be reduced to a few percent at reasonable problem dimensions.

Product Details

ISBN-13:
9783540225409
Publisher:
Springer Berlin Heidelberg
Publication date:
11/23/2004
Series:
Lecture Notes in Economics and Mathematical Systems Series , #548
Edition description:
2005
Pages:
190
Product dimensions:
6.14(w) x 9.21(h) x 0.02(d)

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