A regularization method for ill-posed bilevel optimization problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 19-35.

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://www.numdam.org/articles/10.1051/ro:2006009/}
}
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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. http://www.numdam.org/articles/10.1051/ro:2006009/

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