Neural network based on systematically generated smoothing functions for absolute value equation

Abstract

In this paper, we summarize several systematic ways of constructing smoothing functions and illustrate eight smoothing functions accordingly. Then, based on these systematically generated smoothing functions, a unified neural network model is proposed for solving absolute value equation. The issues regarding the equilibrium point, the trajectory, and the stability properties of the neural network are addressed. Moreover, numerical experiments with comparison are presented, which suggests what kind of smoothing functions work well along with the neural network approach.