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The Levenberg-Marquardt algorithm is a flexible iterative procedure used tosolve non-linear least squares problems. In this work we study how a class ofpossible adaptations of this procedure can be used to solve maximum likelihoodproblems when the underlying distributions are in the exponential family. Weformally demonstrate a local convergence property and we discuss a possibleimplementation of the penalization involved in this class of algorithms.Applications to real and simulated compositional data show the stability andefficiency of this approach.

On the maximization of likelihoods belonging to the exponential family using ideas related to the Levenberg-Marquardt approach