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Modifications and implementation of the ellipsoid algorithm for linear programming

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Abstract

We give some modifications of the ellipsoid algorithm for linear programming and describe a numerically stable implementation. We are concerned with practical problems where user-supplied bounds can usually be provided. Our implementation allows constraint dropping and updates bounds on the optimal value, and should be able to terminate with an indication of infeasibility or with a provably good feasible solution in a moderate number of iterations.

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Authors and Affiliations

  1. The City College, City University of New York, New York, USA

    Donald Goldfarb

  2. Cornell University, Ithaca, NY, USA

    Michael J. Todd

Authors
  1. Donald Goldfarb
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  2. Michael J. Todd
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Additional information

The work of this author was supported in part by the U.S. Army Research Office under Grant DAAG29-77-G-0114 and the National Science Foundation under Grant MCS-8006065.

The work of this author was supported in part by the National Science Foundation under Grant ECS-7921279.

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Goldfarb, D., Todd, M.J. Modifications and implementation of the ellipsoid algorithm for linear programming. Mathematical Programming 23, 1–19 (1982). https://doi.org/10.1007/BF01583776

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  • DOI: https://doi.org/10.1007/BF01583776

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