nonlinear least squares; hybrid methods; trust-region methods; quasi-Newton methods; numerical algorithms; numerical experiments
In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation $A$ of the Jacobian matrix $J$, such that $A^T f = J^T f$. This property allows us to solve a linear least squares problem, minimizing $\|A d + f\|$ instead of solving the normal equation $A^T A d + J^T f = 0$, where $d \in R^n$ is the required direction vector. Computational experiments confirm the efficiency of the new method.