PROOF OF THE CONVERGENCE IN HOPFIELD-TANK MODEL

In this paper, the energy function of Hopfield--Tank is studied in convergence andoptimum rate in Hopfield neural network. Hopfield presented the discrete neural network modal in1982,and the continuous neural network modal in 1984, applying the conception of energy functioninto the research of neural network, and made the lay foundation for the optimization computationaltheory of neural network. In 1985,Hopfield and Tank first used the neural network by softwaresimulation to gain the success of TSP, which drew attention of many researchers, afterward neuralnetwork computation paved a new way for combination optimization. Though many neural networkoptimization algorithms were presented in the following years,there is no doubt that the most basicand important neural network algorithm is Hopfield and Tank algorithm, others are all based on it.So it has important significance to research the theory foundation of Hopfield--Tank algorithm.Although the convergence proof of discrete and continuous Hopfield network have been given byHopfield, the convergence proof of Hopfield-Tank model has not been given up to now. The differencebetween continuous Hopfield network and Hopfield-Tank model is firstly proposed in this paper.Then a convergence proof of Hopfield-Tank model is given. It will make the optimal computationtheory of Hopfield network more complete. In addition. The effect of network parameter 1/τ onminimum point and appropriate value interval is discussed in detail.