Full Length Paper Series A

Mathematical Programming

, Volume 138, Issue 1, pp 309-332

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Solving bilevel programs with the KKT-approach

  • Gemayqzel Bouza AllendeAffiliated withUniversity of Havana
  • , Georg StillAffiliated withUniversity of Twente Email author 


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