In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. We show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to the existence of an error bound for the constraint set, and is also equivalent to a generalized Abadie's qualification condition. These results extend widely previous one like by removing convexity type assumptions on the data.
Institut de Mathématiques de Toulouse, December 2014
View A Characterization of the Lagrange-Karush-Kuhn-Tucker Property