A Retrospective Trust-Region Method for Unconstrained Optimization

         F. Bastin, V. Malmedy, M. Mouffe, Ph. Toint, D. Tomanos

                   Report 07-08 (Maths, FUNDP, Namur)

We introduce  a new trust-region  method for unconstrained  optimization where
the  radius update  is computed  using the  model information  at  the current
iterate  rather than  at  the preceding  one.   The update  is then  performed
according to how well the  current model retrospectively predicts the value of
the  objective function  at last  iterate.  Global  convergence to  first- and
second-order  critical  points  is  proved  under  classical  assumptions  and
preliminary  numerical experiments  on CUTEr  problems indicate  that  the new
method is very competitive.