A geometrical analysis of Hopfield neural network for optimizations

A necessary condition for a HNN (Hopfield neural network) to achieve the global minimum, imposed on the synaptic strengths of HNN, is introduced. The condition is derived based on the geometry of the Lyapunov energy function for the HNN. The synaptic strengths are determined in various ways depending on a subject optimization problem. For instance, for the bearing estimation problem, they are determined by the selected signal set. Hence the condition for the bearing estimation problem is directly related to characteristics of the signal set. Accordingly, based on the signal-set characteristics, it is possible to determine a priori whether the HNN for this problem will achieve the global minimum or not. Also one may select a signal set for which the HNN always achieves the global minimum