Nesterov's accelerated gradient method for nonlinear ill-posed problems with a locally convex residual functional

Abstract

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 convergence analysis of this method for ill-posed problems 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.