A nonmonotone inexact Newton method

Abstract

In this paper, we describe a variant of the inexact Newton method for solving nonlinear systems of equations.We define a nonmonotone inexact Newton step and a nonmonotone backtracking strategy. For this nonmonotone inexact Newton scheme, we present the convergence theorems. Finally, we show how we can apply these strategies to the inexact Newton interior-point method and we present some numerical examples.