  We show that Newton methods for generalized equations are input-to-state
stable with respect to disturbances such as due to inexact computations. We
then use this result to obtain convergence and robustness of a multistep
Newton-type method for multivariate generalized equations. We demonstrate the
usefulness of the results with other applications to nonlinear optimization. In
particular, we provide a new proof for (robust) local convergence of the
augmented Lagrangian method.
