On a new updating rule of the Levenberg-Marquardt parameter
The authors are proposing a change in the Levenberg-Marquardt algorithm for solving systems of nonlinear equations. In the traditional algorithm, the iterate and the specific parameter are updated according to the ratio of the actual reduction to the predicted reduction of the merit function. In the proposed version, the iterate is updated as in the traditional algorithm, while the specific parameter is updated based on the value of the gradient norm of the merit function. It is shown that all limit points of the sequence generated by the new algorithm are stationary points of the merit functions. Moreover, the global convergence and the quadratic convergence under the local error condition are proved.
scientific article; zbMATH DE number 6858887
scientific article