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An Extension of Karmarkar’s Algorithm for Bounded Linear Programming Problems

  • Conference paper
DGOR/NSOR

Part of the book series: Operations Research Proceedings ((ORP,volume 1987))

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Abstract

In this paper we describe Karmarkar’s algorithm and present an extension that works with problems expressed in standard form. We require no a priori knowledge of the optimal value, but assume that the set of optimal solutions is bounded.

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References

  1. Gay, D.M.: Karmarkar’s Algorithm for Problems in Standard Form. Mathematical Programming 37 (1987), 81–90.

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  2. Karmarkar, N.: A New Polynomial-Time Algorithm for Linear Programming. Combinatorica 4 (4) (1984), 373–395.

    Article  Google Scholar 

  3. Khachiyan, L.G.: A Polynomial Algorithm in Linear Programming. Doklady Akademii Nauk SSSR 244(1979), 1093–1096, translated in Soviet Mathematics Doklady 20 (1979), 191-194.

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  4. Padberg, M.: A Different Convergence Proof of the Projective Method for Linear Programming. Operations Research Letters 4 (1986), 253–257.

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  5. Steger, A.: An Extension of Karmarkar’s Algorithm for Bounded Linear Programming Problems. M.S. thesis, State University of New York at Stony Brook (August 1985).

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  6. Todd, M.J. and B.P. Burrell: An Extension of Karmarkar’s Algorithm for Linear Programming Using Dual Variables. Algorithmica 1 (1986), 409–424.

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Author information

Authors and Affiliations

  1. Bonn, Germany

    Angelika Steger

Authors
  1. Angelika Steger
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Editor information

Editors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstraße 7, D-6100, Darmstadt, Deutschland

    Helmut Schellhaas

  2. Department of Mathematics, Agricultural University Wageningen, De Dreijen 8, NL-6703 BC, Wageningen, The Netherlands

    Paul van Beek

  3. Fachbereich Wirtschaftswissenschaft, Johann Wolfgang Goethe-Universität Frankfurt, Mertonstraße 17, D-6000, Frankfurt, Deutschland

    Heinz Isermann

  4. Institut für Betriebswirtschaftslehre, Christian-Albrechts-Universität Kiel, Olshausenstraße 40, D-2300, Kiel, Deutschland

    Reinhart Schmidt

  5. Centre for Quantitative Methods, Nederlandse Philips Bedrijven B.V., P.O. Box 218, NL-5600 MD, Eindhoven, The Netherlands

    Mynt Zijlstra

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© 1988 Springer-Verlag Berlin Heidelberg

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Steger, A. (1988). An Extension of Karmarkar’s Algorithm for Bounded Linear Programming Problems. In: Schellhaas, H., van Beek, P., Isermann, H., Schmidt, R., Zijlstra, M. (eds) DGOR/NSOR. Operations Research Proceedings, vol 1987. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73778-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-73778-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19365-4

  • Online ISBN: 978-3-642-73778-7

  • eBook Packages: Springer Book Archive

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