  We consider the optimistic bilevel optimization problem, known to have a wide
range of applications in engineering, that we transform into a single-level
optimization problem by means of the lower-level optimal value function
reformulation. Subsequently, based on the partial calmness concept, we build an
equation system, which is parameterized by the corresponding partial exact
penalization parameter. We then design and analyze a Levenberg-Marquardt method
to solve this parametric system of equations. Considering the fact that the
selection of the partial exact penalization parameter is a critical issue when
numerically solving a bilevel optimization problem, we conduct a careful
experimental study to this effect, in the context the Levenberg-Marquardt
method, while using the Bilevel Optimization LIBrary (BOLIB) series of test
problems.
