Existence of augmented Lagrange multipliers for cone constrained optimization problems

In this paper, by using an augmented Lagrangian approach, we obtain several sufficient conditions for the existence of augmented Lagrange multipliers of a cone constrained optimization problem in Banach spaces, where the corresponding augmenting function is assumed to have a valley at zero. Furthermore, we deal with the relationship of saddle points, augmented Lagrange multipliers, and zero duality gap property between the cone constrained optimization problem and its augmented Lagrangian dual problem. Copyright Springer Science+Business Media New York 2014