A globally convergent method for nonlinear least-squares problems based on the Gauss-Newton model with spectral correction

Abstract

This work addresses a spectral correction for the Gauss-Newton model in the solution of nonlinear least-squares problems within a globally convergent algorithmic framework. The nonmonotone line search of Zhang and Hager is the chosen globalization tool. We show that the search directions obtained from the corrected Gauss-Newton model satisfy the conditions that ensure the global convergence under such a line search scheme. A numerical study assesses the impact of using the spectral correction for solving two sets of test problems from the literature.

Keywords

• Nonlinear least squares
• spectral parameter
• Gauss-Newton method
• global convergence
• numerical tests