A regularization method for ill-posed bilevel optimization problems

Maïtine Bergounioux (1) , Mounir Haddou (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Mots clés: bi-level; optimization

Domaines: Optimisation et contrôle [math.OC]

Maïtine Bergounioux, Mounir Haddou. A regularization method for ill-posed bilevel optimization problems. RAIRO - Operations Research, 2006, 40, n°1, p. 19-35. ⟨10.1051/ro:2006009⟩. ⟨hal-00021999⟩