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Bilevel programming: A survey

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Abstract.

This paper provides an introductory survey of a class of optimization problems known as bilevel programming. We motivate this class through a simple application, and then proceed with the general formulation of bilevel programs. We consider various cases (linear, linear-quadratic, nonlinear), describe their main properties and give an overview of solution approaches.

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Author notes

  1. Benoít Colson

    Present address: SAMTECH s.a. Liége, Rue des Chasseurs Ardennais, B-4031, Liége, Belgium

Authors and Affiliations

  1. Department of Mathematics, The University of Namur, 5000, Namur, BELGIUM

    Benoít Colson

  2. Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128 Succursale Centre-ville Montreal, H3C 3J7, CANADA

    Patrice Marcotte

  3. Département de mathématiques et de génie industriel, Ecole Polytechnique de Montréal, C.P. 6079 Succursale Centre-ville Montreal, H3C 3A7, (QC), CANADA

    Gilles Savard

Authors
  1. Benoít Colson
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  2. Patrice Marcotte
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  3. Gilles Savard
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Corresponding author

Correspondence to Benoít Colson.

Additional information

Received: April 2005, Revised: May 2005,

AMS classification:

90C05, 90C11, 90C20, 90C27, 90C3D, 65K05

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Colson, B., Marcotte, P. & Savard, G. Bilevel programming: A survey. 4OR 3, 87–107 (2005). https://doi.org/10.1007/s10288-005-0071-0

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  • DOI: https://doi.org/10.1007/s10288-005-0071-0

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