An Algorithm For Solving Nonlinear Least-squares Problems With A New Curvilinear Search

We propose a modification of an algorithm introduced by Martínez (1987) for solving nonlinear least-squares problems. Like in the previous algorithm, after the calculation of an approximated Gauss-Newton direction d, we obtain the next iterate on a two-dimensional subspace which includes d. However, we simplify the process of searching the new point, and we define the plane using a scaled gradient direction, instead of the original gradient. We prove that the new algorithm has global convergence properties. We present some numerical experiments. © 1990 Springer-Verlag.441839