Neural networks with hysteresis type of nonlinearity exhibit global optimization property

Abstract

The minimization of quadratic forms over discrete sets plays a central role in many areas of applications like communication and control theory and pattern recognition. That is why, among the primary interest of neural network (NN) research, the global optimization problem has received distinctive attention. Nevertheless, most of the commonly implemented neural networks either fail to achieve the global optimum like the Hopfield model [3,4], or the necessary amount of computation needed by the optimization is large and time consuming (Boltzmann machine [1]).

As a result, the aim of this paper is to propose a new type of NN capable of quick minimization of quadratic forms. Since the fast optimization of quadratic forms is very much required in communication theory, one of the most promising applications of the new algorithm would be the optimal detection procedure of Gaussian and linearly distorted channels.