The purpose of the present paper is to improve the global convergence results established so far concerning the Augmented Lagrangian Algorithm with exponential penalty function for solving nonlinear programming problems with equality and inequality constraints. We prove global convergence for KKT points under the PAKKT-regular constraint qualifications, which results as a consequence that accumulation points generated by the algorithm are PAKKT points. This convergence result is new for the augmented Lagrangian Method based on the exponential penalty function. An interesting consequence is that the estimates of the Lagrange multipliers computed by the method remain bounded in the presence of the quasi-normality condition. Finally we give optimality and feasibility results for the convex case.