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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. Stanley Zionts, 1969. "The Criss-Cross Method for Solving Linear Programming Problems," Management Science, INFORMS, vol. 15(7), pages 426-445, March.
    3. 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.
    4. Robert G. Bland, 1977. "New Finite Pivoting Rules for the Simplex Method," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 103-107, May.
    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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