Abstract
In this paper, we present a duality approach using conjugacy for a semivectorial bilevel programming problem (S) where the upper and lower levels are vectorial and scalar respectively. This approach uses the Fenchel–Lagrange duality and is given via a regularization of problem (S) and the operation of scalarization. Then, using this approach, we provide necessary optimality conditions for a class of properly efficient solutions of (S). Finally, sufficient optimality conditions are given for (S) regardless of the duality approach. Examples are given for illustration.
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Dedicated to Professor Michel Théra on his 70th birthday.
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Aboussoror, A., Adly, S. & Saissi, F.E. A Duality Approach for a Class of Semivectorial Bilevel Programming Problems. Vietnam J. Math. 46, 197–214 (2018). https://doi.org/10.1007/s10013-017-0268-5
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DOI: https://doi.org/10.1007/s10013-017-0268-5