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A primal—dual infeasible-interior-point algorithm for linear programming

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Abstract

As in many primal—dual interior-point algorithms, a primal—dual infeasible-interior-point algorithm chooses a new point along the Newton direction towards a point on the central trajectory, but it does not confine the iterates within the feasible region. This paper proposes a step length rule with which the algorithm takes large distinct step lengths in the primal and dual spaces and enjoys the global convergence.

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Author information

Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, 2-12-1 Oh-Okayama, Meguro-ku, 152, Tokyo, Japan

    Masakazu Kojima

  2. IBM Almaden Research Center, San Jose, CA, USA

    Nimrod Megiddo

  3. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Nimrod Megiddo

  4. The Institute of Statistical Mathematics, Tokyo, Japan

    Shinji Mizuno

Authors
  1. Masakazu Kojima
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  2. Nimrod Megiddo
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  3. Shinji Mizuno
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Additional information

Part of this research was done when M. Kojima and S. Mizuno visited at the IBM Almaden Research Center. Partial support from the Office of Naval Research under Contract N00014-91-C-0026 is acknowledged.

Supported by Grant-in-Aids for Co-operative Research (03832017) of The Japan Ministry of Education, Science and Culture.

Supported by Grant-in-Aids for Encouragement of Young Scientist (03740125) and Co-operative Research (03832017) of The Japan Ministry of Education, Science and Culture.

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Kojima, M., Megiddo, N. & Mizuno, S. A primal—dual infeasible-interior-point algorithm for linear programming. Mathematical Programming 61, 263–280 (1993). https://doi.org/10.1007/BF01582151

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  • DOI: https://doi.org/10.1007/BF01582151

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