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In this paper, we present two choices of structured spectral gradient methodsfor solving nonlinear least-squares problems. In the proposed methods, thescalar multiple of identity approximation of the Hessian inverse is obtained byimposing the structured quasi-Newton condition. Moreover, we propose a simplestrategy for choosing the structured scalar in the case of negative curvaturedirection. Using the nonmonotone line search with the quadratic interpolationbacktracking technique, we prove that these proposed methods are globallyconvergent under suitable conditions. Numerical experiment shows that themethod is competitive with some recent developed methods.

Structured two-point stepsize gradient methods for nonlinear least squares