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A regularized simplex method

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Abstract

In case of a special problem class, the simplex method can be implemented as a cutting-plane method that approximates a polyhedral convex objective function. In this paper we consider a regularized version of this cutting-plane method, and interpret the resulting procedure as a regularized simplex method. (Regularization is performed in the dual space and only affects the process through the pricing mechanism. Hence the resulting method moves among basic solutions.) We present algorithmic details of this regularized simplex method, and favorable test results with our implementation. For general linear programming problems, we propose a Newton-type approach which requires the solution of a sequence of special problems.

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Acknowledgments

This research and publication have been supported by the European Union and Hungary and co-financed by the European Social Fund through the Project TÁMOP-4.2.2.C-11/1/KONV-2012-0004: National Research Center for the Development and Market Introduction of Advanced Information and Communication Technologies. This source of support is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Informatics, Faculty of Mechanical Engineering and Automation, Kecskemét College, 10 Izsáki út, Kecskemet, 6000, Hungary

    Csaba I. Fábián & Olga Papp

  2. Faculty of Information Technology, University of Pannonia, Veszprém, Hungary

    Krisztián Eretnek

Authors
  1. Csaba I. Fábián
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  2. Krisztián Eretnek
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  3. Olga Papp
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Correspondence to Csaba I. Fábián.

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Fábián, C.I., Eretnek, K. & Papp, O. A regularized simplex method. Cent Eur J Oper Res 23, 877–898 (2015). https://doi.org/10.1007/s10100-014-0344-9

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