A modified BFGS type quasi-Newton method with line search for symmetric nonlinear equations problems

Abstract

In this paper, using approximate gradient of the norm square metric function, we present an inexact MBFGS method with line search for solving symmetric nonlinear equations, which is a generalization of the MBFGS method proposed by Li and Fukushima (2001) for solving smooth unconstrained optimization. The used approximate gradient of the proposed method only requires computing two residuals at every iteration and is easy to obtain by utilizing symmetric structure of the system. We establish global convergence of the proposed method and report some numerical results.