Structured Two-Point Stepsize Gradient Methods for Nonlinear Least Squares

Abstract

In this paper, we present two choices of structured spectral gradient methods for solving nonlinear least squares problems. In the proposed methods, the scalar multiple of identity approximation of the Hessian inverse is obtained by imposing the structured quasi-Newton condition. Moreover, we propose a simple strategy for choosing the structured scalar in the case of negative curvature direction. Using the nonmonotone line search with the quadratic interpolation backtracking technique, we prove that these proposed methods are globally convergent under suitable conditions. Numerical experiment shows that the methods are competitive with some recently developed methods.