A regularization method for ill-posed bilevel optimization problems

Maitine Bergounioux; Mounir Haddou

RAIRO - Operations Research (2006)

  • Volume: 40, Issue: 1, page 19-35
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Bergounioux, Maitine, and Haddou, Mounir. "A regularization method for ill-posed bilevel optimization problems." RAIRO - Operations Research 40.1 (2006): 19-35. <http://eudml.org/doc/249745>.

@article{Bergounioux2006,
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. },
author = {Bergounioux, Maitine, Haddou, Mounir},
journal = {RAIRO - Operations Research},
keywords = {regularization method; ill-posed bilevel problems},
language = {eng},
month = {7},
number = {1},
pages = {19-35},
publisher = {EDP Sciences},
title = {A regularization method for ill-posed bilevel optimization problems},
url = {http://eudml.org/doc/249745},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Bergounioux, Maitine
AU - Haddou, Mounir
TI - A regularization method for ill-posed bilevel optimization problems
JO - RAIRO - Operations Research
DA - 2006/7//
PB - EDP Sciences
VL - 40
IS - 1
SP - 19
EP - 35
AB - 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.
LA - eng
KW - regularization method; ill-posed bilevel problems
UR - http://eudml.org/doc/249745
ER -

References

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