Mathematical Programming

, Volume 138, Issue 1–2, pp 309–332

Solving bilevel programs with the KKT-approach

Open Access
Full Length Paper Series A


Bilevel programs (BL) form a special class of optimization problems. They appear in many models in economics, game theory and mathematical physics. BL programs show a more complicated structure than standard finite problems. We study the so-called KKT-approach for solving bilevel problems, where the lower level minimality condition is replaced by the KKT- or the FJ-condition. This leads to a special structured mathematical program with complementarity constraints. We analyze the KKT-approach from a generic viewpoint and reveal the advantages and possible drawbacks of this approach for solving BL problems numerically.


Bilevel problems KKT-condition FJ-condition Mathematical programs with complementarity constraints Genericity Critical points 

Mathematics Subject Classification

90C30 90C31 

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.University of HavanaHavanaCuba
  2. 2.University of TwenteEnschedeThe Netherlands

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