On the maximization of likelihoods belonging to the exponential family   using ideas related to the Levenberg-Marquardt approach
  The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood problems when the underlying distributions are in the exponential family. We formally demonstrate a local convergence property and we discuss a possible implementation of the penalization involved in this class of algorithms. Applications to real and simulated compositional data show the stability and efficiency of this approach. 
Marco Giordan and Federico Vaggi and Ron Wehrens
stat.CO