Local convergence of augmented Lagrangian methods for composite optimization

Abstract

In this paper, we propose an augmented Lagrangian method for composite optimization with the outer function satisfying the second order epi-regular property. The local convergence and rate of convergence of this algorithm will be proved under the assumptions of the second order sufficient condition via the second order epi-derivative of augmented Lagrangian and the semi-isolated calmness of the solution mapping of perturbed generalized equation formulated from KKT system. For the penalty parameters large enough, we obtain the primal-dual Q-linear convergence rate.