On the Global Convergence of an SLP--Filter Algorithm

             R. Fletcher and S. Leyffer and Ph. L. Toint

                          Report 98/13

A  mechanism for proving  global convergence in filter--type methods for
nonlinear  programming is  described. Such methods  are characterized by
their  use  of  the dominance  concept  of multiobjective  optimization,
instead of a penalty parameter whose  adjustment can be problematic. The
main point of interest is to demonstrate  how convergence for NLP can be
induced without forcing sufficient    descent in a  penalty-type   merit
function.

The proof  technique  is presented in  a  fairly basic  context, but the
ideas involved are likely to  be  more widely applicable. The  technique
allows a range  of specific algorithm  choices  associated with updating
the trust region radius and with feasibility restoration.