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

Authors:
Benoît Colson;Patrice Marcotte;Gilles Savard
Affiliations:
SAMTECH S.A., Liège, Belgium B-4031;CRT and DIRO, Université de Montréal, Montréal, Canada H3C 3J7;Département de Mathématiques et de génie industriel and GERAD, Ecole Polytechnique de Montréal, Montréal, Canada H3C 3A7
Venue:
Computational Optimization and Applications
Year:
2005

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Abstract

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. Numerical experiments tend to confirm the promising behavior of the method.