  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
method is competitive with some recent developed methods.
