A Neural Network Based on a Nonsmooth Equation for a Box Constrained Variational Inequality Problem

Abstract

The variational inequality framework holds significant prominence across various domains including economic finance, network transportation, and game theory. In addition, a novel approach utilizing a neural network model is introduced in the current work to address a box constrained variational inequality problem. Initially, the original problem is reformulated into a nonsmooth equation, following which the neural network model is meticulously devised to tackle this reformulated equation. This study comprehensively investigated inherent characteristics and properties of this neural network model. In addition, employing the Lyapunov function method, stability analysis of the neural network model proposed is rigorously demonstrated in the Lyapunov sense. Furthermore, the efficacy of the proposed technique is substantiated through numerical simulations, providing empirical support for its applicability and effectiveness.