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Extremal Methods and Systems Analysis pp 384–414Cite as

On One-Row Linear Programs

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 174))

Abstract

Motivated by the possibility of improving the efficiency of the dual simplex method, this paper discusses direct solution algorithms for linear programs with upper bounds and generalized upper bounds which apart from bound constraints consist of a single row representing a constraint equation. The close connection between l-row linear programs with upper bounds and the problem of determining weighted medians is demonstrated. The latter problem is known to be of complexity 0(n) wherè n is the number of variables. A solution algorithm of complexity 0(n log n) + 0(k(n-k)) is presented for the 1-row k-mix linear program with generalized upper bounds. This algorithm is based on determining the lower boundary of the convex hull of points in the plane.

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References

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Authors
  1. Christoph Witzgall
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Editors and Affiliations

  1. Department of Operations Research Institute for Management Science and Engineering, The Washington University, 20052, Washington, DC, USA

    Anthony V. Fiacco

  2. Department of Mathematics, Carnegie-Mellon University, 15213, Pittsburgh, PA, USA

    Kenneth O. Kortanek

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© 1980 Springer-Verlag Berlin Heidelberg

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Witzgall, C. (1980). On One-Row Linear Programs. In: Fiacco, A.V., Kortanek, K.O. (eds) Extremal Methods and Systems Analysis. Lecture Notes in Economics and Mathematical Systems, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46414-0_19

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  • DOI: https://doi.org/10.1007/978-3-642-46414-0_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09730-3

  • Online ISBN: 978-3-642-46414-0

  • eBook Packages: Springer Book Archive

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