Fenchel-Lagrange Duality Approach and Optimality Conditions for Strong Bilevel Programming Problems

par Fatima Saissi (Université de Limoges)

vendredi 20 janv. 2017, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

In this talk we give a conjugate duality approach for a strong bilevel programming problem (S). The approach is based on the use of a regularization of problem (S) and the so-called Fenchel-Lagrange duality. We first show that the regularized problem of (S) admits solutions and any accumulation point of a sequence of regularized solutions solves (S). Then, via this duality approach, we establish necessary and sufficient optimality conditions for the regularized problem. Finally, necessary and sufficient optimality conditions are given for the initial problem (S). We note that such an approach which allows us the application of the Fenchel-Lagrange duality to the class of strong bilevel programming problems is new in the literature.