Augmented Lagrangian Filter Method∗

We introduce a filter mechanism to force convergence for augmented Lagrangian methods for nonlinear programming. In contrast to traditional augmented Lagrangian methods, our approach does not require the use of forcing sequences that drive the first-order error to zero. Instead, we employ a filter to drive the optimality measures to zero. Our algorithm is flexible in the sense that it allows for equality constraint quadratic programming steps to accelerate local convergence. We also include a feasibility restoration phase that allows fast detection of infeasible problems. We give a convergence proof that shows that our algorithm converges to first-order stationary points.