NDLI: Scenario reduction in stochastic programming with respect to discrepancy distances

Content Provider	Springer Nature Link
Author	Henrion, René Küchler, Christian Römisch, Werner
Copyright Year	2007
Abstract	Discrete approximations to chance constrained and mixed-integer two-stage stochastic programs require moderately sized scenario sets. The relevant distances of (multivariate) probability distributions for deriving quantitative stability results for such stochastic programs are ℬ-discrepancies, where the class ℬ of Borel sets depends on their structural properties. Hence, the optimal scenario reduction problem for such models is stated with respect to ℬ-discrepancies. In this paper, upper and lower bounds, and some explicit solutions for optimal scenario reduction problems are derived. In addition, we develop heuristic algorithms for determining nearly optimally reduced probability measures, discuss the case of the cell discrepancy (or Kolmogorov metric) in some detail and provide some numerical experience.
Starting Page	67
Ending Page	93
Page Count	27
File Format	PDF
ISSN	09266003
Journal	Computational Optimization and Applications
Volume Number	43
Issue Number	1
e-ISSN	15732894
Language	English
Publisher	Springer US
Publisher Date	2007-11-09
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic programming Chance constraints Two-stage Mixed-integer Scenario reduction Discrepancy Kolmogorov metric Convex and Discrete Geometry Statistics Operations Research/Decision Theory Operations Research, Mathematical Programming Optimization
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Computational Mathematics

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