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The s-monotone index selection rules for pivot algorithms of linear programming

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  • Csizmadia, Zsolt
  • Illés, Tibor
  • Nagy, Adrienn

Abstract

In this paper we introduce the concept of s-monotone index selection rule for linear programming problems. We show that several known anti-cycling pivot rules like the minimal index, Last-In–First-Out and the most-often-selected-variable pivot rules are s-monotone index selection rules. Furthermore, we show a possible way to define new s-monotone pivot rules. We prove that several known algorithms like the primal (dual) simplex, MBU-simplex algorithms and criss-cross algorithm with s-monotone pivot rules are finite methods.

Suggested Citation

  • Csizmadia, Zsolt & Illés, Tibor & Nagy, Adrienn, 2012. "The s-monotone index selection rules for pivot algorithms of linear programming," European Journal of Operational Research, Elsevier, vol. 221(3), pages 491-500.
    • Handle: RePEc:eee:ejores:v:221:y:2012:i:3:p:491-500
    DOI: 10.1016/j.ejor.2012.02.008
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    References listed on IDEAS

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    1. Kurt M. Anstreicher & Tamás Terlaky, 1994. "A Monotonic Build-Up Simplex Algorithm for Linear Programming," Operations Research, INFORMS, vol. 42(3), pages 556-561, June.
    2. Robert G. Bland, 1977. "New Finite Pivoting Rules for the Simplex Method," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 103-107, May.
    3. Stanley Zionts, 1969. "The Criss-Cross Method for Solving Linear Programming Problems," Management Science, INFORMS, vol. 15(7), pages 426-445, March.
    4. Zhang, S., 1997. "New variants of finite criss-cross pivot algorithms for linear programming," Econometric Institute Research Papers EI 9707-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. Illes, Tibor & Terlaky, Tamas, 2002. "Pivot versus interior point methods: Pros and cons," European Journal of Operational Research, Elsevier, vol. 140(2), pages 170-190, July.
    6. BLAND, Robert G., 1977. "New finite pivoting rules for the simplex method," LIDAM Reprints CORE 315, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Konstantinos Paparrizos & Nikolaos Samaras & Angelo Sifaleras, 2015. "Exterior point simplex-type algorithms for linear and network optimization problems," Annals of Operations Research, Springer, vol. 229(1), pages 607-633, June.
    2. Adrienn Csizmadia & Zsolt Csizmadia & Tibor Illés, 2018. "Finiteness of the quadratic primal simplex method when s-monotone index selection rules are applied," 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. 26(3), pages 535-550, September.
    3. Nabli, Hédi & Chahdoura, Sonia, 2015. "Algebraic simplex initialization combined with the nonfeasible basis method," European Journal of Operational Research, Elsevier, vol. 245(2), pages 384-391.

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