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Degeneracy in interior point methods for linear programming: a survey

  • Part I: Surveys
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Abstract

The publication of Karmarkar's paper has resulted in intense research activity into Interior Point Methods (IPMs) for linear programming. Degeneracy is present in most real-life problems and has always been an important issue in linear programming, especially in the Simplex method. Degeneracy is also an important issue in IPMs. However, the difficulties are different in the two methods. In this paper, we survey the various theoretical and practical issues related to degeneracy in IPMs for linear programming.

We survey results, which, for the most part, have already appeared in the literature. Roughly speaking, we shall deal with the effect of degeneracy on the following: the convergence of IPMs, the trajectories followed by the algorithms, numerical performance, and finding basic solutions.

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  1. O. Güler

    Present address: Department of Mathematics and Statistics, University of Maryland Baltimore County, 21228, Baltimore, MD, USA

Authors and Affiliations

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

    O. Güler, D. den Hertog, C. Roos & T. Terlaky

  2. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu Minato-ku, 106, Tokyo, Japan

    T. Tsuchiya

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Partially supported by a research fund of SHELL.

On leave from the Eötvös University, Budapest, and partially supported by OTKA No. 2116.

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Güler, O., den Hertog, D., Roos, C. et al. Degeneracy in interior point methods for linear programming: a survey. Ann Oper Res 46, 107–138 (1993). https://doi.org/10.1007/BF02096259

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