A trust region algorithm for nonlinear bilevel programming

We propose to solve generalized bilevel programs by a trust region approach where the model takes the form of a bilevel program involving a linear program at the upper level and a linear variational inequality at the lower level. By coupling the concepts of trust region and linesearch in a novel way, we obtain an implementable algorithm that converges to a strong stationary point of the original bilevel program. (C) 2001 Elsevier Science B.V. All rights reserved.