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A regularized simplex method

Author

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  • Csaba Fábián
  • Krisztián Eretnek
  • Olga Papp

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. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:23:y:2015:i:4:p:877-898
    DOI: 10.1007/s10100-014-0344-9
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    References listed on IDEAS

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    1. Joseph Elble & Nikolaos Sahinidis, 2012. "Scaling linear optimization problems prior to application of the simplex method," Computational Optimization and Applications, Springer, vol. 52(2), pages 345-371, June.
    2. Csaba Fábián & Gautam Mitra & Diana Roman & Victor Zverovich, 2011. "An enhanced model for portfolio choice with SSD criteria: a constructive approach," Quantitative Finance, Taylor & Francis Journals, vol. 11(10), pages 1525-1534.
    3. Claudia Sagastizábal & Mikhail Solodov, 2012. "Solving generation expansion planning problems with environmental constraints by a bundle method," Computational Management Science, Springer, vol. 9(2), pages 163-182, May.
    4. 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.
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    Cited by:

    1. Botond Bertók & Tibor Csendes & Tibor Illés, 2015. "Editorial," 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 811-813, December.

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