A filter-trust-region method for unconstrained optimization

                  N.I.M. Gould C. Sainvitu and Ph. L. Toint

                                Report TR04-03

A  new  filter-trust-region  algorithm  for  solving  unconstrained  nonlinear
optimization problems is introduced.  Based on the filter technique introduced
by Fletcher  and Leyffer, it extends  an existing technique  of Gould, Leyffer
and  Toint  (SIAM J.  Optim.,  to appear  2004)  for  nonlinear equations  and
nonlinear  least-squares  to  the  fully  general  unconstrained  optimization
problem. The new algorithm is shown  to be globally convergent to at least one
second-order  critical point, and  numerical experiments  indicate that  it is
very competitive with more classical trust-region algorithms.