Scenario reduction in stochastic programming with respect to discrepancy
Please always quote using this URN:urn:nbn:de:0296-matheon-3618
- 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 $\mathcal{B}$-discrepancies, where the class $\mathcal{B}$ of Borel sets depends on their structural properties. Hence, the optimal scenario reduction problem for such models is stated with respect to $\mathcal{B}$-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.
Author: | Rene Henrion, Christian Küchler, Werner Römisch |
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URN: | urn:nbn:de:0296-matheon-3618 |
Referee: | Peter Imkeller |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2006/10/23 |
Release Date: | 2006/10/20 |
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Institute: | Humboldt-Universität zu Berlin |
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS) | |
MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C15 Stochastic programming |
Preprint Number: | 354 |