An Augmented Smoothing Method of L1 -norm Minimization and Its Implementation by Neural Network Model

TL;DR

This paper introduces an augmented smoothing technique for nonlinear L1-norm minimization and demonstrates its effectiveness through a neural network model that successfully finds global solutions.

Contribution

It presents a novel augmented smoothing function and analyzes a neural network approach for solving L1-norm minimization problems.

Findings

Neural network model successfully finds global solutions.

The smoothing function enhances stability and convergence.

Numerical simulations validate the method's effectiveness.

Abstract

In this paper we propose an augmented smoothing function for nonlinear L1 -norm minimization problem and consider a global stability of a gradient-based neural network model to minimize the smoothing function. The numerical simulations show that our smoothing neural network finds successfully the global solution of the L1 -norm minimization problems considered in the simulation.