An augmented Lagrangian method for equality constrained optimization with rapid infeasibility detection capabilities

We present a primal-dual augmented Lagrangian method for solving an equality constrained minimization problem, which is able to rapidly detect infeasibility. The method is based on a modification of the algorithm proposed in [1]. A new parameter is introduced to scale the objective function and, in case of infeasibility, to force the convergence of the iterates to an infea-sible stationary point. It is shown, under mild assumptions, that whenever the algorithm converges to an infeasible stationary point, the rate of convergence is quadratic. This is a new convergence result for the class of augmented La-grangian methods. The global convergence of the algorithm is also analysed. It is also proved that, when the algorithm converges to a stationary point, the properties of the original algorithm [1] are preserved. The numerical experiments show that our new approach is as good as the original one when the algorithm converges to a local minimum, but much more efficient in case of infeasibility.