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

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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.

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Authors and Affiliations

  1. SAMTECH S.A., B-4031, Liège, Belgium

    Benoît Colson

  2. CRT and DIRO, Université de Montréal, CP 6128, Succursale Centre-Ville, Montréal, Québec, Canada, H3C 3J7

    Patrice Marcotte

  3. Département de Mathématiques et de génie industriel and GERAD, Ecole Polytechnique de Montréal, CP 6079, Succursale Centre-Ville, Montréal, Québec, Canada, H3C 3A7

    Gilles Savard

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  1. Benoît Colson
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  2. Patrice Marcotte
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  3. Gilles Savard
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Correspondence to Benoît Colson.

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Colson, B., Marcotte, P. & Savard, G. A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience. Comput Optim Applic 30, 211–227 (2005). https://doi.org/10.1007/s10589-005-4612-4

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