A discrete-time convergence theorem for continuous-state Hopfield networks with self-interaction neurons is proposed. This theorem differs from the previous work by Wang (1997) in that the original updating rule is maintained while the network is still guaranteed to monotonically decrease to a stable state. The relationship between the parameters in a typical class of energy functions is also investigated, and consequently a "guided trial-and-error" technique is proposed to determine the parameter values. The effectiveness of all the theorems proposed in the paper is demonstrated by a large number of computer simulations on the assignment problem and the N-queen problem of different sizes.
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