The MNGNreg toolbox for the regularized solution of nonlinear least-squares problems

Abstract

This paper describes a Matlab toolbox designed to solve nonlinear least-squares problems, with a particular focus on ill-posed cases lacking unique solution, allowing to obtain the minimal-norm solution. The algorithm is based on the Gauss-Newton method, in which the iteration is modified introducing a projection term onto the null space of the Jacobian of the nonlinear function. To address the severe ill-conditioning often encountered in real-world applications, the toolbox also includes some regularization techniques.