Groupe d’études et de recherche en analyse des décisions

# A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience

## Benoît Colson, Patrice Marcotte et Gilles Savard

We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all constraint-defining functions, as well as a quadratic approximation of the lower-level objective. We describe the main features of the algorithm and the resulting software. Preliminary numerical experiments tend to confirm the remarkable behavior of the method.

, 33 pages