On the Convergence of a Filter-SQP Algorithm

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.