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.
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We would like to thank both referee’s for their many valuable comments and for their effort to make the paper more readable.
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Allende, G.B., Still, G. Solving bilevel programs with the KKT-approach. Math. Program. 138, 309–332 (2013). https://doi.org/10.1007/s10107-012-0535-x
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DOI: https://doi.org/10.1007/s10107-012-0535-x
Keywords
- Bilevel problems
- KKT-condition
- FJ-condition
- Mathematical programs with complementarity constraints
- Genericity
- Critical points