On duality in nonconvex vector optimization in Banach spaces using augmented Lagrangians

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.