A neural network for monotone variational inequalities with linear constraints

Variational inequality is a uniform approach for many important optimization and equilibrium problems. Based on the necessary and sufficient conditions for the solution, this Letter presents a neural network model for solving linearly constrained variational inequalities. Several sufficient conditions are provided to ensure the asymptotic stability of the proposing network. There is no need to estimate the Lipschitz constant, and no extra parameter is introduced. Since the sufficient conditions provided in this Letter can be easily checked in practice, these new results have both theoretical and application values. The validity and transient behavior of the proposing neural network are demonstrated by some numerical examples.