Augmented Lagrangian methods with smooth penalty functions

Since the late 1990s, the interest in augmented Lagrangian methods has been revived, and several models with smooth penalty functions for programs with inequality constraints have been proposed, tested and used in a variety of applications. Global convergence results for some of these methods have been published. Here we present a local convergence analysis for a large class of smooth augmented Lagrangian methods based on spectral penalty functions. Our analysis shows that linear convergence in the neighborhood of a local minimum may be expected. Similar to the case of the Hestenes-Powell-Rockafellar augmented Lagrangian, this may be achieved without driving the penalty parameter to zero.