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Exact and inexact penalty methods for the generalized bilevel programming problem

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Abstract

We consider a hierarchical system where a leader incorporates into its strategy the reaction of the follower to its decision. The follower's reaction is quite generally represented as the solution set to a monotone variational inequality. For the solution of this nonconvex mathematical program a penalty approach is proposed, based on the formulation of the lower level variational inequality as a mathematical program. Under natural regularity conditions, we prove the exactness of a certain penalty function, and give strong necessary optimality conditions for a class of generalized bilevel programs.

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Authors and Affiliations

  1. Département d'Informatique et de Recherche Opérationnelle, Université de Montréal, Succursale Centre-Ville, C.P. 6128, H3C 3J7, Montréal, Québec, Canada

    P. Marcotte

  2. Centre de Recherche sur les Transports, Université de Montréal, H3C 3J7, Montréal, Québec, Canada

    D. L. Zhu

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  1. P. Marcotte
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  2. D. L. Zhu
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Marcotte, P., Zhu, D.L. Exact and inexact penalty methods for the generalized bilevel programming problem. Mathematical Programming 74, 141–157 (1996). https://doi.org/10.1007/BF02592209

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  • DOI: https://doi.org/10.1007/BF02592209

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