A structured diagonal Hessian approximation method with evaluation complexity analysis for nonlinear least squares

This work proposes a Jacobian-free strategy for addressing large-scale nonlinear least-squares problems, in which structured secant conditions are used to define a diagonal approximation for the Hessian matrix. Proper safeguards are devised to ensure descent directions along the generated sequence. Worst-case evaluation analysis is provided within the framework of a non-monotone line search. Numerical experiments contextualize the proposed strategy, by addressing structured problems from the literature, also solved by related and recently presented conjugate gradient and multivariate spectral gradient strategies, as well as the classic Fletcher–Reeves conjugate gradient, and the Raydan–Barzilai–Borwein methods. The comparative computational results show a favorable performance of the proposed approach, mainly as far as robustness is concerned.