A BFGS method using inexact gradient for general nonlinear equations

Abstract

A globally and superlinearly convergent BFGS methods is introduced to solve general nonlinear equations without computing exact gradient. Compared with existing Gauss-Newton-based BFGS type methods, the proposed method does not require conditions such as sysmmetry on the underlying function. Moreover, it can be suitably adjusted to solve nonlinear least squares problems and still guarantee global convergence. Some numerical results are reported are reported to show its efficiency.