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New necessary and sufficient optimality conditions for strong bilevel programming problems

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Abstract

In this paper we are interested in a strong bilevel programming problem (S). For such a problem, we establish necessary and sufficient global optimality conditions. Our investigation is based on the use of a regularization of problem (S) and some well-known global optimization tools. These optimality conditions are new in the literature and are expressed in terms of \(\max \)–\(\min \) conditions with linked constraints.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable remarks and suggestions that improved the quality of the paper.

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Authors and Affiliations

  1. Laboratoire LMC, Faculté Polydisciplinaire de Safi, Université Cadi Ayyad, B.P. 4162, Sidi Bouzid, Safi, Morocco

    Abdelmalek Aboussoror

  2. Laboratoire XLIM, Faculté des Sciences et Techniques, UMR-CNRS 6172, 123 Avenue Albert Thomas, 87060, Limoges Cedex, France

    Samir Adly

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  1. Abdelmalek Aboussoror
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  2. Samir Adly
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Correspondence to Samir Adly.

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Aboussoror, A., Adly, S. New necessary and sufficient optimality conditions for strong bilevel programming problems. J Glob Optim 70, 309–327 (2018). https://doi.org/10.1007/s10898-018-0606-5

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