Use of the

In this work a new stabilization scheme for the Gauss-Newton method is defined, where the minimum norm solution of the linear least-squares problem is normally taken as search direction, and the standard Gauss-Newton equation is suitably modified only at a subsequence of iterates. Moreover, the stepsize is computed by means of a nonmonotone line search technique. The global convergence of the proposed algorithm model is proved under standard assumptions, and the superlinear rate of convergence is ensured for the zero-residual case. A specific implementation algorithm is described, where the use of the pure Gauss-Newton iteration is conditioned to the progress made in the minimization process by controlling the stepsize. The results of a computational experimentation performed on a set of standard test problems are reported.