Global exponential stability of recurrent neural networks for solving optimization and related problems

Global exponential stability is a desirable property for dynamic systems. T his paper studies the global exponential stability of several existing recu rrent neural networks for solving linear programming problems, convex progr amming problems with interval constraints, convex programming problems with nonlinear constraints, and monotone variational inequalities. In contrast to the existing results on global exponential stability, the present result s do not require additional conditions on the weight matrices of recurrent neural networks and improve some existing conditions for global exponential stability. Therefore, the stability results in this paper further demonstr ate the superior convergence properties of the existing neural networks for optimization.