On the convergence of neural network for higher order programming

Hopfield network, which was firstly proposed in 1982, can deal with only quadratic programming. For higher-order programming, a higher-order network architecture is necessary. Although generalized higher-order Hopfield network is a straight forward solution, the network convergence property has to be restudied before it can be put into application. Inheriting from Hopfield network, the existence of non-zero self-reinforcing terms is expected to give rise to network oscillation. A reshaping strategy, which is speculated from similar strategy for Hopfield network, is derived to guarantee generalized higher-order Hopfield network´s convergence. Numerical example is given to illustrate its validity.