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Disjunctive cuts for continuous linear bilevel programming

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Abstract

This work shows how disjunctive cuts can be generated for a bilevel linear programming problem (BLP) with continuous variables. First, a brief summary on disjunctive programming and bilevel programming is presented. Then duality theory is used to reformulate BLP as a disjunctive program and, from there, disjunctive programming results are applied to derive valid cuts. These cuts tighten the domain of the linear relaxation of BLP. An example is given to illustrate this idea, and a discussion follows on how these cuts may be incorporated in an algorithm for solving BLP.

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Authors and Affiliations

  1. Départment de Mathématiques et de Génie Industriel – GERAD, École Polytechnique de Montréal, 3000, Côte-Sainte-Catherine, Montréal, QC, Canada, H3T 2A7

    Charles Audet & Gilles Savard

  2. Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal, succ. Centre-ville, C.P. 6079, Montréal, QC, Canada, H3C 3A7

    Charles Audet, Jean Haddad & Gilles Savard

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  1. Charles Audet
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  2. Jean Haddad
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  3. Gilles Savard
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Correspondence to Charles Audet.

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Audet, C., Haddad, J. & Savard, G. Disjunctive cuts for continuous linear bilevel programming. Optimization Letters 1, 259–267 (2007). https://doi.org/10.1007/s11590-006-0024-3

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