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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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, LSO, Sidi Mohamed Ben Abdellah University, Dhar El Mahraz, Fes, Morocco

    N. Gadhi & M. El idrissi

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  1. N. Gadhi
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  2. M. El idrissi
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Correspondence to M. El idrissi.

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Gadhi, N., idrissi, M.E. An equivalent one level optimization problem to a semivectorial bilevel problem. Positivity 22, 261–274 (2018). https://doi.org/10.1007/s11117-017-0511-z

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  • DOI: https://doi.org/10.1007/s11117-017-0511-z

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