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A regularization method for ill-posed bilevel optimization problems

Published online by Cambridge University Press:  01 July 2006

Maitine Bergounioux  and
Mounir Haddou
Maitine Bergounioux
Affiliation:
MAPMO-UMR 6628, Fédération Denis Poisson, Université d'Orléans, BP 6759, 45067 Orléans Cedex 2, France; maitine.bergounioux@univ-orleans.fr, mounir.haddou@univ-orleans.fr
Mounir Haddou
Affiliation:
MAPMO-UMR 6628, Fédération Denis Poisson, Université d'Orléans, BP 6759, 45067 Orléans Cedex 2, France; maitine.bergounioux@univ-orleans.fr, mounir.haddou@univ-orleans.fr
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Abstract

We present a regularization method to approach a solution of the pessimistic formulation of ill-posed bilevel problems. This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and responses. We prove existence of approximated solutions, give convergence result using Hoffman-like assumptions. We end with objective value error estimates.

Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 1 , January 2006 , pp. 19 - 35
Copyright
© EDP Sciences, 2006

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