On the global convergence of the inexact semi-smooth Newton method for absolute value equation

TL;DR

This paper analyzes the global convergence of an inexact semi-smooth Newton method for solving absolute value equations, establishing theoretical convergence results and demonstrating practical effectiveness through numerical experiments.

Contribution

It provides the first comprehensive analysis of global convergence for the inexact semi-smooth Newton method applied to AVE, including theoretical proofs and numerical validation.

Findings

Global Q-linear convergence is proven under certain assumptions.

Numerical experiments confirm the practical viability of the method.

The method is effective for solving absolute value equations in practice.

Abstract

In this paper, we investigate global convergence properties of the inexact nonsmooth Newton method for solving the system of absolute value equations (AVE). Global $Q$-linear convergence is established under suitable assumptions. Moreover, we present some numerical experiments designed to investigate the practical viability of the proposed scheme.