Duality and penalization in optimization via an augmented Lagrangian function with applications (Q1024250)

To establish good candidates that an augmented Lagrangian functions reaches a zero duality gap, is a nice challenge in optimization, This paper provides an instance where it is possible to reach such goals. After introducing the concepts of a valley at 0 augmenting function and the corresponding augmented Lagrangian problem, it is established the existence of solutions of a primal problem and its valley at 0 augmented Lagrangian problem in a reflexive Banach space. Then, the zero duality gap property is stated between the primal problem and the valley at 0 augmented Lagrangian dual problem. Finally, the results are applied to an inequality and equality constrained optimization problem in infinite-dimensional spaces and variational problems in Sobolev spaces.