Convergence Results on Proximal Method of Multipliers in Nonconvex Programming

We describe a primal-dual application of the proximal point algorithm to nonconvex minimization problems. Motivated by the work of Spingarn and more recently by the work of Kaplan and Tichatschke about the proximal point methodology in nonconvex optimization. This paper discusses some local results in two directions. The first one concerns the application of the proximal method of multipliers to a general nonconvex problem under second order optimality conditions. Secondly we show that without the second order statements, local convergence is obtained for a particular class of nonconvex programs. keywords: Augmented Lagrangian, nonconvex programming, proximal regularization. AMS subject classification: 65K05, 90C30.