On the convergence of derivative-free methods 
                    for unconstrained optimization

               A. R. Conn  K. Scheinberg   Ph. L. Toint

                    Report 96/10   17 December 1996


The  purpose  of this paper  is  to  examine a  broad class of derivative-free
trust-region methods for unconstrained optimization inspired by  the proposals
of Powell (1994) and to derive a general  framework in which reasonable global
convergence  results can be obtained.  The developments make extensive  use of
an interpolation  error bound  derived  by  Sauer  and  Xu  in the  context of
multivariate polynomial interpolation.

This paper is dedicated to Professor M. J. D. Powell for his 60th birthday.