Cellular non-linear networks for minimization of functionals. Part 1: Theoretical aspects

摘要

A method for the defintion of cellular non-linear networks able to find approximate minima of rather a large class of continuous functionals is proposed and discussed form a theoretical point of view. The method is based on the spatial discretization of continuous functionals and on the theory of potential functions for resistive circuits. The discretization of the continuous functional is obtained by resorthing to the finite difference method or to the finite element method. The spatial discretization converts a functional into a function of a finite set of variables. By exploiting the theory of potential functions for resistive circuits, form such a function one can derive a lumped circuit that makes it possible to find an approximate minimum of the given functional.