On the convergence of a regularizing Levenberg-Marquardt scheme for nonlinear ill-posed problems

In this note we study the convergence of the Levenberg-Marquardt regularization scheme for nonlinear ill-posed problems. We consider the case that the initial error satisfies a source condition. Our main result shows that if the regularization parameter does not grow too fast (not faster than a geometric sequence), then the scheme converges with optimal convergence rates. Our analysis is based on our recent work on the convergence of the exponential Euler regularization scheme [3].