par Kleinert, Thomas;Labbé, Martine
;Plein, Fränk
;Schmidt, Martin
Référence Optimization Letters
Publication Publié, 2020-11-11
![](/vufind/images/ULB/publications_list.png)
![](/vufind/images/ULB/publications_list.png)
Référence Optimization Letters
Publication Publié, 2020-11-11
Article révisé par les pairs
Résumé : | Linear bilevel optimization problems are often tackled by replacing the linear lower-level problem with its Karush–Kuhn–Tucker conditions. The resulting single-level problem can be solved in a branch-and-bound fashion by branching on the complementarity constraints of the lower-level problem’s optimality conditions. While in mixed-integer single-level optimization branch-and-cut has proven to be a powerful extension of branch-and-bound, in linear bilevel optimization not too many bilevel-tailored valid inequalities exist. In this paper, we briefly review existing cuts for linear bilevel problems and introduce a new valid inequality that exploits the strong duality condition of the lower level. We further discuss strengthened variants of the inequality that can be derived from McCormick envelopes. In a computational study, we show that the new valid inequalities can help to close the optimality gap very effectively on a large test set of linear bilevel instances. |