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Bilevel mixed-integer linear programs and the zero forcing set

Pierre-Louis Poirion(poirion***at***lix.polytechnique.fr)
Sonia Toubaline(toubaline***at***lix.polytechnique.fr)
Claudia D'Ambrosio(dambrosio***at***lix.polytechnique.fr)
Leo Liberti(liberti***at***lix.polytechnique.fr)

Abstract: We study a class of bilevel binary linear programs with lower level variables in the upper-level constraints. Under certain assumptions, we prove that the problem can be reformulated as a single-level binary linear program, and propose a finitely terminating cut generation algorithm to solve it. We then relax the assumptions by means of a general row-and-column generation framework. As an illustrative application we consider the minimum zero forcing set problem, a variant of the dominating set problem, and prove that it can be written as a binary linear bilevel program. Finally, we perform some numerical experiments to showcase the practical applicability of our methods.

Keywords: BIlevel programming; zero forcing set

Category 1: Integer Programming (Other )

Category 2: Integer Programming (Cutting Plane Approaches )

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation:

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Entry Submitted: 11/22/2015
Entry Accepted: 11/22/2015
Entry Last Modified: 11/22/2015

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