CONVERGENCE RATE OF THE AUGMENTED LAGRANGIAN SQP METHOD

In this paper, the augmented Lagrangian SQP method is considered for t he numerical solution of optimization problems with equality constrain ts. The problem is formulated in a Hilbert space setting. Since the au gmented Lagrangian SQP method is a type of Newton method for the nonli near system of necessary optimality conditions, it is conceivable that q-quadratic convergence can be shown to hold locally in the pair (x, lambda). Our interest lies in the convergence of the variable x alone. We improve convergence estimates for the Newton multiplier update whi ch does not satisfy the same convergence properties in x as for exampl e the least-square multiplier update. We discuss these updates in the context of parameter identification problems. Furthermore, we extend t he convergence results to inexact augmented Lagrangian methods. Numeri cal results for a control problem are also presented.