Bilevel optimization problems are hierarchical problems with a
constraint set which is a subset of the graph of the solution set mapping of
a second optimization problem. To investigate their properties and derive solution
algorithms, their transformation into single-level ones is necessary. For
this, various approaches have been developed. The rst and most often used
approach is to replace the lower level problem using its Karush-Kuhn-Tucker
conditions. It has been shown that this results in a nonconvex optimization
problem which is equivalent to the bilevel optimization problem if a global
optimal solution is searched for. In case of local optimal solutions this is no
longer the case: a local optimal solution of the single-level problem does not
need to be related to a local optimal solution of the bilevel optimization problem.
In this article transformation approaches using dierent dual problems for
the lower level optimization problem are investigated. The resulting nonconvex
single-level optimization problems are again not equivalent to the bilevel
optimization problem provided their local optimal solutions are considered.