**Auteurs : **Phan Quoc Khanh, Tran Hue Nuong & Michel
Théra

**Titre : **On duality in nonconvex vector optimization in
Banach spaces using augmented Lagrangians

**Nbre de pages : **22

**Document :** Article (PDF)

**Résumé :** This paper shows how the use of
penalty functions in terms of projections on the constraint cones,
which are orthogonal in the sense of Birkhoff, permits to establish
augmented Lagrangians and to define a dual problem of a given
nonconvex vector optimization problem. Then the weak duality always
holds. Using the quadratic growth condition together with the
inf-stability or a kind of Rockafellar's stability called stability
of degree two, we derive strong duality results between the properly
efficient solutions of the two problems. A strict converse duality
result is proved under an additional convexity assumption, which is
shown to be essential.

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