Levenberg-marquardt revisited and parameter tuning of river regression models

The Levenberg-Marquardt method is well known for solving nonlinear least squares problems. This method is mostly used in the context of overdetermined systems. In this paper it is shown that suitable implementations with respect to underdetermined systems can be defined. The resulting method is equipped with a new effective non-monotone strategy and it is proved that, when the residual tends to zero, a sufficient descent condition is obtained with minimal computational cost. The method is applied to the problem of parameter fitting of regression models based on Neural Networks for natural rivers.