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A Monotonic Build-Up Simplex Algorithm for Linear Programming

Author

Listed:
  • Kurt M. Anstreicher

    (University of Iowa, Iowa City, Iowa)

  • Tamás Terlaky

    (Delft University of Technology Delft, The Netherlands)

Abstract

We devise a new simplex pivot rule which has interesting theoretical properties. Beginning with a basic feasible solution, and any nonbasic variable having a negative reduced cost the pivot rule produces a sequence of pivots such that ultimately the originally chosen nonbasic variable enters the basis, and all reduced costs which were originally nonnegative remain nonnegative. The pivot rule thus monotonically builds up to a dual feasible, and hence optimal, basis. A surprising property is that the pivot sequence results in intermediate bases which are neither primal nor dual feasible. We prove the correctness of the procedure, and relate it to other pivoting rules for linear programming.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:3:p:556-561
    DOI: 10.1287/opre.42.3.556
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    Cited by:

    1. Paparrizos, Konstantinos & Samaras, Nikolaos & Stephanides, George, 2003. "An efficient simplex type algorithm for sparse and dense linear programs," European Journal of Operational Research, Elsevier, vol. 148(2), pages 323-334, July.
    2. 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.
    3. 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.
    4. 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.

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