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

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  • Csaba Fábián
  • Olga Papp
  • Krisztián Eretnek

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. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Csaba Fábián & Olga Papp & Krisztián Eretnek, 2013. "Implementing the simplex method as a cutting-plane method, with a view to regularization," Computational Optimization and Applications, Springer, vol. 56(2), pages 343-368, October.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:2:p:343-368
    DOI: 10.1007/s10589-013-9562-7
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    References listed on IDEAS

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    1. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
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    3. Maros, Istvan, 2003. "A generalized dual phase-2 simplex algorithm," European Journal of Operational Research, Elsevier, vol. 149(1), pages 1-16, August.
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    6. István Maros, 2003. "A General Pricing Scheme for the Simplex Method," Annals of Operations Research, Springer, vol. 124(1), pages 193-203, November.
    7. J. L. Goffin & A. Haurie & J. P. Vial, 1992. "Decomposition and Nondifferentiable Optimization with the Projective Algorithm," Management Science, INFORMS, vol. 38(2), pages 284-302, February.
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    1. Csaba Fábián & Krisztián Eretnek & Olga Papp, 2015. "A regularized simplex method," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 877-898, December.

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