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Basis exchange characterizations for the simplex son algorithm for LP/embedded networks

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Mathematical Programming Essays in Honor of George B. Dantzig Part I

Part of the book series: Mathematical Programming Studies ((MATHPROGRAMM,volume 24))

Abstract

The simplex special ordered network (SON) algorithm is a partitioning method for solving LP problems with embedded network structure. The algorithm derives from a theoretical characterization of the network topology of the basis embodied in a specially constructed master basis tree. In this paper we show that the topology of the master basis tree and the rules by which it can admissibly be restructured can be characterized by seven mutually exclusive and collectively exhaustive basis exchange cases. Further, these seven cases will always keep the network portion of the basis at its maximum dimension.

This research was supported in part by the U.S. Department of Transportation contract DOT-TX-06-0040, by the Office of Naval Research contract N00014-78-C-0222, by the Center for Business Decision Analysis, The University of Texas at Austin and by the David Bruton Jr. Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.

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Author information

Authors and Affiliations

  1. Department of Management Science, University of Colorado, 80302, Boulder, CO, USA

    Fred Glover

  2. Department of General Business, Graduate School of Business, The University of Texas, 78712, Austin, TX, USA

    Darwin Klingman

Authors
  1. Fred Glover
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  2. Darwin Klingman
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Editor information

R. W. Cottle

Additional information

Dedicated to George B. Dantzig on the occasion of his seventieth birthday.

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© 1985 The Mathematical Programming Society, Inc.

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Glover, F., Klingman, D. (1985). Basis exchange characterizations for the simplex son algorithm for LP/embedded networks. In: Cottle, R.W. (eds) Mathematical Programming Essays in Honor of George B. Dantzig Part I. Mathematical Programming Studies, vol 24. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0121048

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  • DOI: https://doi.org/10.1007/BFb0121048

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00918-1

  • Online ISBN: 978-3-642-00919-8

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