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A cutting plane method from analytic centers for stochastic programming

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Abstract

The stochastic linear programming problem with recourse has a dual block-angular structure. It can thus be handled by Benders' decomposition or by Kelley's method of cutting planes; equivalently the dual problem has a primal block-angular structure and can be handled by Dantzig-Wolfe decomposition—the two approaches are in fact identical by duality. Here we shall investigate the use of the method of cutting planes from analytic centers applied to similar formulations. The only significant difference form the aforementioned methods is that new cutting planes (or columns, by duality) will be generated not from the optimum of the linear programming relaxation, but from the analytic center of the set of localization.

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Authors and Affiliations

  1. Département d'Économie Commerciale et Industrielle, Université de Genève, Genève, Switzerland

    O. Bahn, O. du Merle & J. -P. Vial

  2. GERAD, Faculty of Management, McGill University, Montreal, Canada

    J. -L. Goffin

Authors
  1. O. Bahn
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  2. O. du Merle
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  3. J. -L. Goffin
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  4. J. -P. Vial
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Additional information

This research has been supported by the Fonds National de la Recherche Scientifique Suisse (grant # 12-26434.89), NSERC-Canada and FCAR-Quebec.

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Bahn, O., du Merle, O., Goffin, J.L. et al. A cutting plane method from analytic centers for stochastic programming. Mathematical Programming 69, 45–73 (1995). https://doi.org/10.1007/BF01585552

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  • DOI: https://doi.org/10.1007/BF01585552

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