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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.
@article{RO_2006__40_1_19_0,
author = {Bergounioux, Maitine and Haddou, Mounir},
title = {A regularization method for ill-posed bilevel optimization problems},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {19--35},
publisher = {EDP-Sciences},
volume = {40},
number = {1},
year = {2006},
doi = {10.1051/ro:2006009},
mrnumber = {2248420},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ro:2006009/}
}
TY - JOUR AU - Bergounioux, Maitine AU - Haddou, Mounir TI - A regularization method for ill-posed bilevel optimization problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2006 SP - 19 EP - 35 VL - 40 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ro:2006009/ DO - 10.1051/ro:2006009 LA - en ID - RO_2006__40_1_19_0 ER -
%0 Journal Article %A Bergounioux, Maitine %A Haddou, Mounir %T A regularization method for ill-posed bilevel optimization problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2006 %P 19-35 %V 40 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ro:2006009/ %R 10.1051/ro:2006009 %G en %F RO_2006__40_1_19_0
Bergounioux, Maitine; Haddou, Mounir. A regularization method for ill-posed bilevel optimization problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 19-35. doi: 10.1051/ro:2006009
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