  In this paper, we consider Nesterov's Accelerated Gradient method for solving
Nonlinear Inverse and Ill-Posed Problems. Known to be a fast gradient-based
iterative method for solving well-posed convex optimization problems, this
method also leads to promising results for ill-posed problems. Here, we provide
a convergence analysis for ill-posed problems of this method based on the
assumption of a locally convex residual functional. Furthermore, we demonstrate
the usefulness of the method on a number of numerical examples based on a
nonlinear diagonal operator and on an inverse problem in auto-convolution.
