On the Barzilai–Borwein gradient methods with structured secant equation for nonlinear least squares problems

Abstract

ABSTRACT We propose structured spectral gradient algorithms for solving nonlinear least squares problems based on a modified structured secant equation. The idea was to integrate more details of the Hessian of the objective function into the standardized spectral parameters with the goal of improving numerical efficiency. We safeguard the structured spectral parameters to avoid negative curvature search direction. The sequence of the search direction generated by the respective proposed algorithm satisfies the sufficient descent condition. Using a nonmonotone line search strategy, we establish the global convergence of the proposed algorithms under some standard assumptions. Numerical experiments on some benchmark test problems show that the proposed algorithms are efficient and outperform some existing competitors.