An Augmented Lagrangian Method for Constrained Optimization Problems in Hilbert Spaces

The purpose of this paper is to develop general properties of an augmented Lagrangian function for a class of constrained optimization problems in Hilbert spaces. We establish necessary and sufficient conditions for the existence of global (local) saddle points of this augmented Lagrangian function which allows to a global (local) exactness. We also establish a zero duality gap property between the primal problem and its augmented Lagrangian dual problem. An application for a constrained nonlinear optimal control problems of parabolic equations is also presented.