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.

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