Some Inexact Version of the Iterative Exponential Method for Solving Nonsmooth Equations

Abstract

This paper presents an inexact version of an exponential iterative method designed for solving nonlinear equations F(x)=0, where the function F is only locally Lipschitz continuous. The proposed algorithm is completely new as an essential extension of the iterative exponential method for solving nonsmooth equations. The method with backtracking is globally and superlinearly convergent under some mild assumptions imposed on F. The presented results of the numerical computations confirm both the theoretical properties of the new method and its practical effectiveness.

Keywords

• nonsmooth equation
• exponential formula
• inexact Newton method
• Bouligand subdifferential
• superlinear convergence