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Finiteness of the quadratic primal simplex method when s-monotone index selection rules are applied

Author

Listed:
  • Adrienn Csizmadia

    (FICO UK)

  • Zsolt Csizmadia

    (FICO UK)

  • Tibor Illés

    (Budapest University of Technology and Economics)

Abstract

This paper considers the primal quadratic simplex method for linearly constrained convex quadratic programming problems. Finiteness of the algorithm is proven when $${\mathbf {s}}$$ s -monotone index selection rules are applied. The proof is rather general: it shows that any index selection rule that only relies on the sign structure of the reduced costs/transformed right hand side vector and for which the traditional primal simplex method is finite, is necessarily finite as well for the primal quadratic simplex method for linearly constrained convex quadratic programming problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:cejnor:v:26:y:2018:i:3:d:10.1007_s10100-018-0523-1
    DOI: 10.1007/s10100-018-0523-1
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    References listed on IDEAS

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    1. De Panne, C & Whinston, Andrew, 1969. "The Symmetric Formulation of the Simplex Method for Quadratic Programming," Econometrica, Econometric Society, vol. 37(3), pages 507-527, July.
    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. Akkeles, Arif A. & Balogh, Laszlo & Illes, Tibor, 2004. "New variants of the criss-cross method for linearly constrained convex quadratic programming," European Journal of Operational Research, Elsevier, vol. 157(1), pages 74-86, August.
    4. 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.
    5. 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.
    6. Stanley Zionts, 1969. "The Criss-Cross Method for Solving Linear Programming Problems," Management Science, INFORMS, vol. 15(7), pages 426-445, March.
    7. 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.
    8. 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.
    9. 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. Botond Bertók & Tibor Csendes & Tibor Jordán, 2019. "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. 27(2), pages 325-327, June.
    2. Marianna Eisenberg-Nagy & Tibor Illés & Gábor Lovics, 2019. "Market exchange models and geometric programming," 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. 27(2), pages 415-435, June.
    3. Marijana Zekić-Sušac & Rudolf Scitovski & Goran Lešaja, 2018. "CEJOR special issue of Croatian Operational Research Society," 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 531-534, September.
    4. Darvay, Zsolt & Illés, Tibor & Rigó, Petra Renáta, 2022. "Predictor-corrector interior-point algorithm for P*(κ)-linear complementarity problems based on a new type of algebraic equivalent transformation technique," European Journal of Operational Research, Elsevier, vol. 298(1), pages 25-35.

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