Generalized Bounds for Convex Multistage Stochastic Programs
Series
Lecture Notes in Economics and Mathematical Systems
ISBN
3-540-22540-4
Type
book
Date Issued
2005
Author(s)
Kuhn, Daniel
Abstract
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.
Language
English
Keywords
Approximation Technique
Convex Multistage Stochastic Program
Nonconvexities
Numerical Solution
Regularization
HSG Classification
not classified
Refereed
No
Publisher
Springer
Publisher place
Berlin
Number
548
Start page
190
Subject(s)
Division(s)
Eprints ID
7052