Local Convergence Of Inexact Augmented Lagrangian Methods For Composite Optimization Problems

Composite optimization problems are an important kind of optimization problems,which have a wide range of applications in many fields.Many practical optimization problem models involve composite functions,and the composite optimization problem model provides a unified framework for the development and analysis of algorithm solving technology,so it has received a lot of attention and research.In this paper,the composite optimization problem is characterized by a composite optimization problem in which the outer function is a second order epi-regular function compounding a second order continuous differentiable function.We propose an augmented Lagrangian algorithm for this composite optimization problem.The convergence of the algorithm is obtained under the assumption that the second order sufficient condition defined by the second order epi-derivative of the augmented Lagrangian function and the solution map of the disturbance equation of the KKT system are semi-isolated calm.For the penalty parameters large enough,we obtain the primal-dual Q-linear convergence rate.