An assessment of non-monotone linesearch techniques 
        for unconstrained optimization

              Philippe L. Toint

                Report 94/14

The  purpose  of  this  paper  is  to  discuss  the
potential of non-monotone  techniques for enforcing
convergence    of    unconstrained     minimization
algorithms from  starting  points distant  from the
solution.    Linesearch    based   algorithms   are
considered for  both small and large problems,  and
extensive  numerical  experiments  show  that  this
potential is sometimes considerable.  A new variant
is  introduced  in  order  to  limit  some  of  the
identified  drawbacks of  the existing  techniques.
This  variant  is  again  numerically  tested   and
appears to be competitive.  Finally,  the impact of
preconditioning   on  the  considered  methods   is
examined.