Theories on the Hopfield neural networks

The Hopfield neural networks are well suited to solving large-scale optimization problems, but their convergence characteristics are not theoretically known. The author clarifies, by an eigenvalue analysis, conditions for converging to a vertex, a point on the edge, or an interior point of the hypercube. Taking the traveling salesman problem as an example, the author shows how to determine the weighting factors of the constraints and the objective function in the energy. Numerical calculations demonstrate that optimal or near-optimal solutions are obtained for 6, 10, and 13 cities.<>