Bilevel programming: A survey |
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| Authors: | Benoít Colson Patrice Marcotte Gilles Savard |
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| Institution: | (1) Department of Mathematics, The University of Namur, 5000 Namur, BELGIUM;(2) Present address: SAMTECH s.a. Liége, Rue des Chasseurs Ardennais, B-4031 Liége, Belgium;(3) Département d’Informatique et de Recherche Opérationnelle, Université de Montréal, C.P. 6128 Succursale Centre-ville Montreal, H3C 3J7, CANADA;(4) Département de mathématiques et de génie industriel, Ecole Polytechnique de Montréal, C.P. 6079 Succursale Centre-ville Montreal, H3C 3A7 (QC), CANADA |
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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.Received: April 2005, Revised: May 2005, AMS classification:
90C05, 90C11, 90C20, 90C27, 90C3D, 65K05 |
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| Keywords: | Bilevel programming Mathematical programs with equilibrium constraints Nonlinear programming Optimal pricing |
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