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Implementing the simplex method as a cutting-plane method, with a view to regularization

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Abstract

We show that the simplex method can be interpreted as a cutting-plane method, assuming that a special pricing rule is used. This approach is motivated by the recent success of the cutting-plane method in the solution of special stochastic programming problems.

We focus on the special linear programming problem of finding the largest ball that fits into a given polyhedron. In a computational study we demonstrate that ball-fitting problems have such special characteristics which indicate their utility in regularization schemes.

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Acknowledgements

The authors wish to thank István Maros, Tamás Terlaky, Tamás Szántai, András Prékopa and the anonymous Referees for many constructive remarks and valuable comments that led to substantial improvement of the paper.

This research and publication have been supported by the European Union and Hungary and co-financed by the European Social Fund through the projects 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, and TÁMOP-4.2.2.C-11/1/KONV-2012-0012: “Smarter Transport”—IT for Co-operative Transport Systems. These sources of support are gratefully acknowledged.

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Authors and Affiliations

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

    Csaba I. Fábián & Olga Papp

  2. Doctoral School in Mathematics, Eötvös Loránd University, Budapest, Hungary

    Csaba I. Fábián & Olga Papp

  3. Faculty of Informatics, Eötvös Loránd University, Budapest, Hungary

    Krisztián Eretnek

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  1. Csaba I. Fábián
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Correspondence to Csaba I. Fábián.

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Fábián, C.I., Papp, O. & Eretnek, K. Implementing the simplex method as a cutting-plane method, with a view to regularization. Comput Optim Appl 56, 343–368 (2013). https://doi.org/10.1007/s10589-013-9562-7

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