Mathematical Programming

, Volume 138, Issue 1, pp 309–332

Solving bilevel programs with the KKT-approach

Authors

  • Gemayqzel Bouza Allende
    • University of Havana
    • University of Twente
Open AccessFull Length Paper Series A

DOI: 10.1007/s10107-012-0535-x

Cite this article as:
Allende, G.B. & Still, G. Math. Program. (2013) 138: 309. doi:10.1007/s10107-012-0535-x

Abstract

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.

Keywords

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