Structured two-point stepsize gradient methods for nonlinear least squares

TL;DR

This paper introduces two structured spectral gradient methods for nonlinear least squares, utilizing quasi-Newton conditions and a simple scalar choice strategy, with proven global convergence and competitive numerical performance.

Contribution

The paper proposes novel structured spectral gradient methods with a new scalar selection strategy and convergence analysis for nonlinear least squares problems.

Findings

Methods are globally convergent under certain conditions.

Numerical experiments show competitiveness with recent methods.

Proposed strategies improve efficiency in solving nonlinear least squares.

Abstract

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.