Structured diagonal Gauss-Newton method for nonlinear least squares

This work proposes a structured diagonal Gauss-Newton algorithm for solving zero residue nonlinear least-squares problems. The matrix corresponding to the Gauss-Newton direction is approximated with a diagonal matrix that satisfies the structured secant condition. Using a derivative-free Armijo-type line search with some appropriate conditions, we prove that the proposed algorithm converges globally. Furthermore, the algorithm achieved R-linear convergence rate for zero residue problems. Numerical result shows that the algorithm is competitive with the existing algorithms in the literature.