Solving Variational Inequality Problems with Linear Constraints Based on a Novel Recurrent Neural Network

Abstract

Variational inequalities with linear inequality constraints are widely used in constrained optimization and engineering problems. By extending a new recurrent neural network [14], this paper presents a recurrent neural network for solving variational inequalities with general linear constraints in real time. The proposed neural network has one-layer projection structure and is amenable to parallel implementation. As a special case, the proposed neural network can include two existing recurrent neural networks for solving convex optimization problems and monotone variational inequality problems with box constraints, respectively. The proposed neural network is stable in the sense of Lyapunov and globally convergent to the solution under a monotone condition of the nonlinear mapping without the Lipschitz condition. Illustrative examples show that the proposed neural network is effective for solving this class of variational inequality problems.