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New optimality conditions and a scalarization approach for a nonconvex semi-vectorial bilevel optimization problem

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Abstract

In this paper, we are concerned with the optimistic formulation of a semivectorial bilevel optimization problem. Introducing a new scalarization technique for multiobjective programs, we transform our problem into a scalar-objective optimization problem by means of the optimal value reformulation and establish its theoretical properties. Detailed necessary conditions, to characterize local optimal solutions of the problem, were then provided, while using the weak basic CQ together with the generalized differentiation calculus of Mordukhovich. Our approach is applicable to nonconvex problems and is different from the classical scalarization techniques previously used in the literature and the conditions obtained are new.

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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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  1. LAMA, Department of Mathematics, Sidi Mohamed Ben Abdellah University, Fès, Morocco

    L. Lafhim

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  1. L. Lafhim
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Correspondence to L. Lafhim.

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Lafhim, L. New optimality conditions and a scalarization approach for a nonconvex semi-vectorial bilevel optimization problem. Positivity 24, 395–413 (2020). https://doi.org/10.1007/s11117-019-00685-1

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