A mechanism for proving global convergence infilter-type methods for nonlinear programming is described. Such methods are characterized by their use of the dominance concept of multi objective 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 decent 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.
NA\183, Department of Mathematics,University of Dundee, UK, August, 1998.