Cellular non-linear networks for minimization of functionals. Part I: Theoretical aspects

A method for the definition of cellular non-linear networks able to find ap proximate minima of rather a large class of continuous functionals is propo sed and discussed from a theoretical point of view. The method is based on the spatial discretization of continuous functionals and on the theory of p otential functions for resistive circuits. The discretization of the contin uous functionals is obtained by resorting to the finite difference method o r to the finite element method. The spatial discretization converts a funct ional into a function of a finite set of variables. By exploiting the theor y of potential functions for resistive circuits, from such a function one c an derive a lumped circuit that makes it possible to find an approximate mi nimum of the given functional. Copyright (C) 2001 John Wiley & Sons, Ltd.