  The Levenberg-Marquardt algorithm is one of the most popular algorithms for
finding the solution of nonlinear least squares problems. Across different
modified variations of the basic procedure, the algorithm enjoys global
convergence, a competitive worst case iteration complexity rate, and a
guaranteed rate of local convergence for both zero and nonzero small residual
problems, under suitable assumptions. We introduce a novel Levenberg-Marquardt
method that matches, simultaneously, the state of the art in all of these
convergence properties with a single seamless algorithm. Numerical experiments
confirm the theoretical behavior of our proposed algorithm.
