Signal space interpretations of Hopfield neural network for optimization

A necessary condition for a Hopfield neural network (HNN) to achieve the global minimum is introduced. The condition is obtained from a geometrical analysis of the Lyapunov energy function for HNNs. The condition can be effectively used to test, for an optimization problem under consideration, whether an HNN will generate the global optimum solution for the problem without the local optimum problem or not. The condition can also serve as a measure of the likelihood of achieving the global minimum when the condition is violated. For the bearing estimation problem, the HNN is interpreted as reaching the global minimum in the signal space