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Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach

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Abstract

In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Positivity, 2019. https://doi.org/10.1007/s11117-019-00685-1) is erroneous. Using techniques from variational analysis, we propose other proofs to detect necessary optimality conditions in terms of Karush–Kuhn–Tucker multipliers. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first order necessary optimality conditions are then given in the smooth setting while using the generalized differentiation calculus of Mordukhovich.

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Acknowledgements

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

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Authors and Affiliations

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

    Nazih Abderrazzak Gadhi, Mohammed El idrissi & Khadija Hamdaoui

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  1. Nazih Abderrazzak Gadhi
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  2. Mohammed El idrissi
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  3. Khadija Hamdaoui
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Correspondence to Mohammed El idrissi.

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Gadhi, N.A., El idrissi, M. & Hamdaoui, K. Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach. Positivity 24, 1111–1134 (2020). https://doi.org/10.1007/s11117-019-00723-y

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