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On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm

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Abstract

The primal projective algorithm for linear programs with unknown optimal objective function value is extended to the case where one uses a weighted Karmarkar potential function. This potential is defined with respect to a strict lower bound to the optimum. The minimization of this potential when the lower bound is kept fixed, yields a primal and a dual feasible solution. The dual solution is the weighted analytic center of a certain dual polytope. Finally one exhibits a pair of homothetic dual ellipsoids that extends results obtained by Sonnevend, Todd, Ye, Freund and Anstreicher.

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Authors and Affiliations

  1. GERAD, Faculty of Management, McGill University, Samuel Bronfman Building, H3A 1G5, Montréal, Qué., Canada

    J. L. Goffin

  2. Département d'économie commerciale et industrielle, Université de Genève, Switzerland

    J. P. Vial

Authors
  1. J. L. Goffin
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  2. J. P. Vial
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Additional information

This research has been supported by NSERC-Canada, FCAR-Quebec and FNRS-Switzerland.

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Goffin, J.L., Vial, J.P. On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm. Mathematical Programming 60, 81–92 (1993). https://doi.org/10.1007/BF01580602

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  • DOI: https://doi.org/10.1007/BF01580602

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