Structured spectral algorithm with a nonmonotone line search for nonlinear least squares

This work proposes a matrix-free algorithm incorporating structured spectral parameters with a nonmonotone line search for solving nonlinear least squares problems. The structured Hessian matrix associated with the Newton's-like direction is approximated with a scalar multiple of identity. The scalar is a convex combination of the spectral parameters such that the structured quasi-Newton condition is approximately satisfied. Using a nonmonotone line search with some appropriate conditions, the global convergence of the sequence generated by the proposed algorithm is presented. The numerical result shows that the algorithm is competitive with the existing algorithms in the literature. (c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This work proposes a matrix-free algorithm that combines structured spectral parameters with a nonmonotone line search to solve nonlinear least squares problems. The structured Hessian matrix associated with the Newton's-like direction is approximated with a scalar multiple of identity, where the scalar is a convex combination of the spectral parameters, approximately satisfying the structured quasi-Newton condition. By using a nonmonotone line search with appropriate conditions, the global convergence of the sequence generated by the proposed algorithm is presented. The numerical result demonstrates the competitiveness of the algorithm compared to existing algorithms in the literature.