A regularization method for ill-posed bilevel optimization problems

Details A regularization method for ill-posed bilevel optimization problems A regularization method for ill-posed bilevel optimization problems

2006-03-31

arxiv.org/abs/math/0603741v1

RAIRO Operations Research 40 (2006) n?1, p. 19-35

Mathematics

Optimization and Control

19 pages

Scientific paper

10.1051/ro:2006009

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.

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