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Optimality conditions for pessimistic bilevel problems using convexificator

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Abstract

The purpose of this paper is to study the pessimistic version of bilevel programming problems in finite-dimensional spaces. Problems of this type are intrinsically nonsmooth (even for smooth initial data). By using optimal value function, we transform the initial problem into a generalized minimax optimization problem. Using convexificators, first-order necessary optimality conditions are then established. An example that illustrates our findings is also given.

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Acknowledgements

Our sincere acknowledgements to the anonymous referees for their insightful remarks and suggestions. The second author has been supported by the Alexander-von Humboldt foundation.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Technical University Bergakademie Freiberg, Freiberg, Germany

    S. Dempe

  2. LAMA, Department of Mathematics, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Fez, Morocco

    N. Gadhi & L. Lafhim

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  1. S. Dempe
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  2. N. Gadhi
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  3. L. Lafhim
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Correspondence to N. Gadhi.

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Dempe, S., Gadhi, N. & Lafhim, L. Optimality conditions for pessimistic bilevel problems using convexificator. Positivity 24, 1399–1417 (2020). https://doi.org/10.1007/s11117-020-00737-x

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