Journal of Global Optimization

, Volume 70, Issue 2, pp 309–327 | Cite as

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.

Keywords

Two-level optimization Convergence of multifunctions Reverse convex problems Global optimization tools 

Mathematics Subject Classification

91A65 90C31 90C26 

Notes

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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Laboratoire LMC, Faculté Polydisciplinaire de SafiUniversité Cadi AyyadSidi BouzidMorocco
  2. 2.Laboratoire XLIM, Faculté des Sciences et TechniquesUMR-CNRS 6172Limoges CedexFrance

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