Mathematical Programming

, Volume 138, Issue 1, pp 309–332

Solving bilevel programs with the KKT-approach


  • Gemayqzel Bouza Allende
    • University of Havana
    • University of Twente

DOI: 10.1007/s10107-012-0535-x


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


We would like to thank both referee’s for their many valuable comments and for their effort to make the paper more readable.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Copyright information

© The Author(s) 2012