  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.
