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Links Between Linear Bilevel and Mixed 0–1 Programming Problems

Author

Listed:
  • C. Audet

    (École Polytechnique de Montréal)

  • P. Hansen

    (École des Hautes Études Commerciales and GERAD)

  • B. Jaumard

    (École Polytechnique de Montréal and GERAD)

  • G. Savard

    (École Polytechnique de Montréal and GERAD)

Abstract

We study links between the linear bilevel and linear mixed 0–1 programming problems. A new reformulation of the linear mixed 0–1 programming problem into a linear bilevel programming one, which does not require the introduction of a large finite constant, is presented. We show that solving a linear mixed 0–1 problem by a classical branch-and-bound algorithm is equivalent in a strong sense to solving its bilevel reformulation by a bilevel branch-and-bound algorithm. The mixed 0–1 algorithm is embedded in the bilevel algorithm through the aforementioned reformulation; i.e., when applied to any mixed 0–1 instance and its bilevel reformulation, they generate sequences of subproblems which are identical via the reformulation.

Suggested Citation

  • C. Audet & P. Hansen & B. Jaumard & G. Savard, 1997. "Links Between Linear Bilevel and Mixed 0–1 Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 273-300, May.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:2:d:10.1023_a:1022645805569
    DOI: 10.1023/A:1022645805569
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    References listed on IDEAS

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    1. J. A. Tomlin, 1971. "Technical Note—An Improved Branch-and-Bound Method for Integer Programming," Operations Research, INFORMS, vol. 19(4), pages 1070-1075, August.
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