Supervised learning of the steady-state outputs in generalized cellular networks

It is shown that the supervised learning of the steady-state outputs in a generalized cellular network (CNN) is, in general, equivalent to a kind of constrained optimization problem. The objective function, also known as the error function, is a measure of the distance between the sets of desired steady-state outputs and actual ones. The constraints are due to a set of design requirements which have to be met for providing the qualitative and quantitative properties for the network. The approach presented uses the idea of the penalty function method in optimization theory where the constrained optimization problem is transformed into an unconstrained one by adding to the error function the terms corresponding to the constraints. A gradient descent algorithm is proposed for solving the resulting unconstrained backpropagation algorithm into the generalized CNN.