Convergence analysis of discrete time recurrent neural networks for linear variational inequality problem

We study the convergence of a class of discrete recurrent neural networks to solve linear variational inequality problem (LVIP). LVIP has important applications in engineering and economics. Not only the network's exponential convergence for the case of positive definite matrix is proved, but its global convergence for positive semidefinite matrix is also proved. Conditions are derived to guarantee the convergences of the network. Comprehensive examples are discussed and simulated to illustrate the results.