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Decomposition of Structured Linear Programs Based on Analytical Centers

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Decision Processes in Economics

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 353))

Abstract

The aim of this paper is to review the celebrated decomposition scheme of Dantzig and Wolfe and to explain how it can be modified in view of a more efficient implementation based on analytical centers. Our purpose here is mainly didactic: we seek to provide a non technical introduction to the subject matter.

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References

  1. G. B. Dantzig et P. Wolfe, “The decomposition algorithm for linear programming”, Econometrica 29 (4), (1961), 767–778.

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  2. J.-L. Goffin, A. Haurie et J.-P. Vial, “Decomposition and nondifferentiable optimization with the projective algorithm”, manuscript, Département d’économie commerciale et industrielle, University of Geneva (July 1989).

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  3. J.-l. Goffin et J.-P. Vial, “Cutting planes and column generation techniques with the projective algorithm”, manuscript, Département d’économie commerciale et industrielle, University of Geneva (1988), to appear in Journal of Optimization Theory and Applications.

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  4. G. Sonnevend, “An analytical center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming”’, in Lecture Notes in Control and Information Sciences 84 (Springer, New York, 1985) 866–876.

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Author information

Authors and Affiliations

  1. Département d’économie commerciale et industrielle, Université de Genève, 2, rue de Candolle, CH-1211, Genève 4, Switzerland

    J.-Ph. Vial

Authors
  1. J.-Ph. Vial
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Editor information

Editors and Affiliations

  1. Department of Political Economics, University of Modena, I-41100, Modena, Italy

    Gianni Ricci

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© 1991 Springer-Verlag Berlin Heidelberg

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Vial, JP. (1991). Decomposition of Structured Linear Programs Based on Analytical Centers. In: Ricci, G. (eds) Decision Processes in Economics. Lecture Notes in Economics and Mathematical Systems, vol 353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45686-2_14

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  • DOI: https://doi.org/10.1007/978-3-642-45686-2_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53592-8

  • Online ISBN: 978-3-642-45686-2

  • eBook Packages: Springer Book Archive

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