In this paper, we present a new
method of approximating the minimum of a functional, J, defined on a prehilbert
space and subject to constraints of the form ψi(x) = 0,1 ≦ i ≦ p, where the
ψi are also functionals on the space. The method generates a convergent
sequence of approximations using the gradients of J and ψi. However, it is
not a steepest descent procedure with respect to J. A theorem is proven
which establishes the convergence of the approximating sequence to the
minimum.