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Scenario reduction in stochastic programming with respect to discrepancy distances

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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.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, 10117, Berlin, Germany

    René Henrion

  2. Institute of Mathematics, Humboldt-University Berlin, 10099, Berlin, Germany

    Christian Küchler & Werner Römisch

Authors
  1. René Henrion
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  2. Christian Küchler
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  3. Werner Römisch
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Correspondence to René Henrion.

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Henrion, R., Küchler, C. & Römisch, W. Scenario reduction in stochastic programming with respect to discrepancy distances. Comput Optim Appl 43, 67–93 (2009). https://doi.org/10.1007/s10589-007-9123-z

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  • DOI: https://doi.org/10.1007/s10589-007-9123-z

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