A globally convergent inexact Newton method with a new choice for the forcing term

In inexact Newton methods for solving nonlinear systems of equations, an approximation to the step sk of the Newton's system J(xk)s=−F(xk) is found. This means that sk must satisfy a condition like ‖ F(xk)+J(xk)sk ‖ ≤ ηk ‖ F(xk) ‖ for a forcing term ηk ∈ [0,1). Possible choices for ηk have already been presented. In this work, a new choice for ηk is proposed. The method is globalized using a robust backtracking strategy proposed by Birgin et al., and its convergence properties are proved.