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.