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Finding an interior point in the optimal face of linear programs

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Abstract

We study the problem of finding a point in the relative interior of the optimal face of a linear program. We prove that in the worst case such a point can be obtained in O(n 3 L) arithmetic operations. This complexity is the same as the complexity for solving a linear program. We also show how to find such a point in practice. We report and discuss computational results obtained for the linear programming problems in the NETLIB test set.

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Authors and Affiliations

  1. Department of Industrial Engineering and Management Sciences, Northwestern University, 60208-3119, Evanston, IL, USA

    Sanjay Mehrotra

  2. Department of Management Sciences, The University of Iowa, Iowa City, IA, USA

    Yinyu Ye

Authors
  1. Sanjay Mehrotra
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  2. Yinyu Ye
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Additional information

Research supported in part by NSF Grant CCR-8810107, CCR-9019469 and a grant from GTE Laboratories.

Research supported in part by NSF Grant DDM-8922636 and NSF Coop. Agr. No. CCR-8809615 through Rice University.

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Mehrotra, S., Ye, Y. Finding an interior point in the optimal face of linear programs. Mathematical Programming 62, 497–515 (1993). https://doi.org/10.1007/BF01585180

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  • DOI: https://doi.org/10.1007/BF01585180

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