Links Between Linear Bilevel and Mixed 0–1 Programming Problems
C. Audet,
P. Hansen,
B. Jaumard and
G. Savard
Additional contact information
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
Journal of Optimization Theory and Applications, 1997, vol. 93, issue 2, No 2, 273-300
Abstract:
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.
Keywords: Bilevel programming; mixed 0–1 programming; embedded algorithms; branch-and-bound methods (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:93:y:1997:i:2:d:10.1023_a:1022645805569
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DOI: 10.1023/A:1022645805569
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