On the Convergence of a Filter-SQP Algorithm

            Roger Fletcher, Sven Leyffer and Philippe Toint

                            Report 00/15

A mechanism for proving gobal convergence in filter-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
paremeter 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 relates to a
prototypical algorithm, within which is allowed a range of specific algorithm
choices associated with the Hessian matrix representation, updating the trust
region radius, and feasibility restoration.