Analysis of time-varying cellular neural networks for quadratic global optimization

The algorithm for quadratic global optimization performed by a cellular neural network (CNN) with a slowly varying slope of the output characteristic (see References 1 and 2) is analysed. It is shown that the only CNN which finds the global minimum of a quadratic function for any values of the input parameters is the network composed by only two cells. If the dimension is higher than two, even the CNN described by the simplest one-dimensional space-invariant template Â=[A1, A0, A1], fails to find the global minimum in a subset of the parameter space. Extensive simulations show that the CNN described by the above three-element template works correctly within several parameter ranges; however, if the parameters are chosen according to a random algorithm, the error rate increases with the number of cells. © 1998 John Wiley & Sons, Ltd.