On the Convergence Properties of a Second-Order Augmented Lagrangian Method for Nonlinear Programming Problems with Inequality Constraints

Abstract

The objective of this paper is to conduct a theoretical study on the convergence properties of a second-order augmented Lagrangian method for solving nonlinear programming problems with both equality and inequality constraints. Specifically, we utilize a specially designed generalized Newton method to furnish the second-order iteration of the multipliers and show that when the linear independent constraint qualification and the strong second-order sufficient condition hold, the method employed in this paper is locally convergent and possesses a superlinear rate of convergence, although the penalty parameter is fixed and/or the strict complementarity fails.