Zero duality and saddle points of a class of augmented Lagrangian functions in constrained non-convex optimization

Abstract

In this article, we introduce a unified class of augmented Lagrangian functions for constrained non-convex optimization problems which include many types of the augmented Lagrangians. We first get the zero duality gap property between the primal problem and the augmented Lagrangian dual problem. Then, under second-order sufficiency conditions, we prove that this class of augmented Lagrangian functions possesses local saddle points. Finally, we show the existence of global saddle points without requiring the compactness of X and the uniqueness of the global solution.