The primal-dual augmented Lagrangian function provides a link between augmented Lagrangian methods and stabilized sequential quadratic programming (sSQP) methods. Each sSQP iteration requires the solution of a (possibly nonconvex) quadratic program defined in terms of both the primal and the dual variables. Until recently, research on sSQP has focused primarily on their rate of convergence to a local solution. In this talk we discuss the local convergence properties of a globally convergent primal-dual SQP method that uses the primal-dual augmented Lagrangian merit function in conjunction with a descent direction and a direction of negative curvature. If necessary, the algorithm convexifies the QP subproblem, but, under certain weak assumptions, it can be shown that the solution of the subproblem is eventually identical to a solution of the conventional sSQP subproblem. As a result, the strong local convergence results of sSQP are shown to apply to the proposed globally convergent method.