A Neural Network for Solving Inverse Quasi-Variational Inequalities

TL;DR

This paper introduces a neural network approach to solve inverse quasi-variational inequalities, proving convergence, stability, and providing numerical validation for the method.

Contribution

It establishes the existence, uniqueness, and stability of solutions for a neural network designed for inverse quasi-variational inequalities, with convergence analysis and numerical examples.

Findings

Neural network converges to the unique solution

Network is globally asymptotically stable

Discretized network sequence converges strongly

Abstract

We study the existence and uniqueness of solutions to the inverse quasi-variational inequality problem. Motivated by the neural network approach to solving optimization problems such as variational inequality, monotone inclusion, and inverse variational problems, we consider a neural network associated with the inverse quasi-variational inequality problem, and establish the existence and uniqueness of a solution to the proposed network. We prove that every trajectory of the proposed neural network converges to the unique solution of the inverse quasi-variational inequality problem and that the network is globally asymptotically stable at its equilibrium point. We also prove that if the function which governs the inverse quasi-variational inequality problem is strongly monotone and Lipschitz continuous, then the network is globally exponentially stable at its equilibrium point. We discretize the network and show that the sequence generated by the discretization of the network converges strongly to a solution of the inverse quasi-variational inequality problem under certain assumptions on the parameters involved. Finally, we provide numerical examples to support and illustrate our theoretical results.