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Primal-dual target-following algorithms for linear programming

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Abstract

In this paper, we propose a method for linear programming with the property that, starting from an initial non-central point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow paths that in the limit are tangential to the central path. Together with the convergence analysis, we provide a general framework which enables us to analyze various primal-dual algorithms in the literature in a short and uniform way.

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Authors and Affiliations

  1. Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    B. Jansen, C. Roos & T. Terlaky

  2. Department of Commercial and Industrial Economics, University of Geneva, Geneva, Switzerland

    J. -Ph. Vial

Authors
  1. B. Jansen
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  2. C. Roos
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  3. T. Terlaky
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  4. J. -Ph. Vial
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Additional information

This work was completed with the support of a research grant from SHELL. The first author is supported by the Dutch Organization for Scientific Research (NWO), Grant No. 611-304-028. The third author is on leave from the Eötvös University, Budapest, and partially supported by OTKA No. 2116. The fourth author is supported by the Swiss National Foundation for Scientific Research, Grant No. 12-34002.92.

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Jansen, B., Roos, C., Terlaky, T. et al. Primal-dual target-following algorithms for linear programming. Ann Oper Res 62, 197–231 (1996). https://doi.org/10.1007/BF02206817

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