Disjunctive cuts for continuous linear bilevel programming

Author: Audet Charles   Haddad Jean   Savard Gilles  

Publisher: Springer Publishing Company

ISSN: 1862-4472

Source: Optimization Letters, Vol.1, Iss.3, 2007-06, pp. : 259-267

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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.