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.