Positivity

, Volume 22, Issue 1, pp 261–274 | Cite as

An equivalent one level optimization problem to a semivectorial bilevel problem

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Abstract

In this paper, we are concerned with a bilevel optimization problem \(P_{0}\), where the lower level problem is a vector optimization problem. First, we give an equivalent one level optimization problem for which the nonsmooth Mangasarian–Fromowitz constraint qualification can hold at feasible solution. Using a special scalarization function, one deduces necessary optimality condition for the initial problem.

Keywords

Bilevel optimization Convex function Clarke subdifferential Optimal value function Optimality conditions 

Mathematics Subject Classification

Primary 90C29 90C26 90C70 Secondary 49K99 

Notes

Acknowledgements

Thanks are due to the anonymous referees for the careful reading and the improvements they bring to our paper.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsLSO, Sidi Mohamed Ben Abdellah UniversityFesMorocco

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