This paper deals to the study and approximation of stiff delay differential equations based on an analysis of a certain error functional. In seeking to minimize the error by using standard descent schemes, the procedure can never get stuck in local minima, but will always and steadily decrease the error until getting to the solution sought. Starting with an initial approximation to the solution, we improve it, adding the solution of some associated linear problems, in such a way that the error is decreased. The performance is expected very good due to the fact that we can use very robust methods to approximate linear stiff delay differential equations.