  We consider a bilevel program involving a linear lower level problem with
left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker
reformulation of the problem and subsequently build a tractable optimization
problem with linear constraints by means of a partial exact penalization. A
semismooth system of equations is then generated from the later problem and a
Newton-type method is developed to solve it. Finally, we illustrate the
convergence and practical implementation of the algorithm on the optimal
toll-setting problem in transportation networks.
