Recent progress in unconstrained nonlinear 
                   optimization without derivatives
 
                 A. R. Conn K. Scheinberg Ph. L. Toint
 
                              Report 97/12

We present an introduction to a new class of derivative free methods for
unconstrained optimization.  We  start by discussing the motivation  for
such methods and why they are in  high demand by practitioners.  We then
review the past   developments  in this  field, before  introducing  the
features  that characterize the newer algorithms.   In  the context of a
trust  region framework, we focus  on techniques  that ensure a suitable
``geometric quality''  of the considered  models.   We then outline  the
class of  algorithms  based  on  these   techniques,  as well as   their
respective merits.   We finally conclude the paper  with a discussion of
open questions and perspectives.