A trust region algorithm for nonlinear bilevel programming

Authors:
P. Marcotte;G. Savard;D. L. Zhu
Affiliations:
DIRO and CRT, Université de Montréal, CP 6128, succursale Centre-ville, Montréal, QC, Canada H3C 3J7;GERAD and Département de mathématiques et génie industriel, ícole Polytechnique, C.P. 6079, succursale Centre-ville, Montréal, QC, Canada H3C 3A7;CRT, Université de Montréal, CP 6128, succursale Centre-ville, Montréal, QC, Canada H3C 3J7 and Fudan University, Shanghai, China
Venue:
Operations Research Letters
Year:
2001

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Abstract

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.