New optimality conditions for bilevel programs by using an exact separation principle

  • N. GadhiEmail author
  • S. Dempe
  • M. El Idrissi
Original Paper


In this paper, we are concerned with a bilevel optimization problem \(\left( P\right) \). Reducing it into a one-level nonlinear and nonsmooth program using an exact separation theorem we give necessary optimality conditions in terms of Fréchet subdifferentials and Fréchet normal cones.


Bilevel optimzation Compact set Fréchet subdifferential Fréchet normal cone Optimality conditions 



This work has been supported by the Alexander-von-Humboldt foundation.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dhar El Mehrez, Department of MathematicsLSO, Sidi Mohamed Ben Abdellah UniversityFesMorocco
  2. 2.Department of Mathematics and Computers SciencesTechnical University Bergakademie FreibergFreibergGermany

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