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Determination of optimal vertices from feasible solutions in unimodular linear programming

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Abstract

In this paper we consider a linear programming problem with the underlying matrix unimodular, and the other data integer. Given arbitrary near optimum feasible solutions to the primal and the dual problems, we obtain conditions under which statements can be made about the value of certain variables in optimal vertices. Such results have applications to the problem of determining the stopping criterion in interior point methods like the primal—dual affine scaling method and the path following methods for linear programming.

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Authors and Affiliations

  1. Department of Prediction and Control, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan

    Shinji Mizuno

  2. Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI, USA

    Romesh Saigal

  3. Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA, USA

    James B. Orlin

Authors
  1. Shinji Mizuno
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  2. Romesh Saigal
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  3. James B. Orlin
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Additional information

This author's research is partially supported by NSF grant DDM-8921835 and Airforce Grant AFSOR-88-0088.

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Mizuno, S., Saigal, R. & Orlin, J.B. Determination of optimal vertices from feasible solutions in unimodular linear programming. Mathematical Programming 59, 23–31 (1993). https://doi.org/10.1007/BF01581235

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  • DOI: https://doi.org/10.1007/BF01581235

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