Necessary Conditions for Stability of Solutions in Recurrent Neural Networks

A procedure that defines values of constraint weight parameters of single-layer relaxation-type recurrent neural networks for establishing stability of all solutions for an optimization problem is introduced. Application to the Traveling Salesman optimization problem, using the discrete dynamics Hopfield network as the recurrent neural network algorithm, is shown to illustrate the procedure. Simulation results confirm that the procedure establishes stability of solutions in the state space of the recurrent neural network dynamics. This effectively leads the network to converge to a solution after each relaxation.