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The Generalized Mangasarian-Fromowitz Constraint Qualification and Optimality Conditions for Bilevel Programs

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Abstract

We consider the optimal value reformulation of the bilevel programming problem. It is shown that the Mangasarian-Fromowitz constraint qualification in terms of the basic generalized differentiation constructions of Mordukhovich, which is weaker than the one in terms of Clarke’s nonsmooth tools, fails without any restrictive assumption. Some weakened forms of this constraint qualification are then suggested, in order to derive Karush-Kuhn-Tucker type optimality conditions for the aforementioned problem. Considering the partial calmness, a new characterization is suggested and the link with the previous constraint qualifications is analyzed.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technische Universität Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe & Alain B. Zemkoho

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  1. Stephan Dempe
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  2. Alain B. Zemkoho
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Correspondence to Stephan Dempe.

Additional information

Communicated by V.F. Demyanov.

The authors are grateful to an anonymous referee for pointing an error in an example of an earlier version and for some useful comments, which helped to improve the quality of the paper. We would also like to acknowledge the valuable comments and suggestions from the editors, which vastly contributed to improve the presentation of the paper. Finally, the second author acknowledges the support by the Deutscher Akademischer Austausch Dienst (DAAD).

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Dempe, S., Zemkoho, A.B. The Generalized Mangasarian-Fromowitz Constraint Qualification and Optimality Conditions for Bilevel Programs. J Optim Theory Appl 148, 46–68 (2011). https://doi.org/10.1007/s10957-010-9744-8

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