On the global convergence of an SLP-filter algorithm

Roger Fletcher (fletchermaths.dundee.ac.uk)
Sven Leyffer (sleyffermaths.dundee.ac.uk)
Phillipe L. Toint (philippe.tointfundp.ac.be)

Abstract: 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 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.

Keywords: Nonlinear programming, global convergence, filter, multiobjective optimization, SLP

Category 1: Nonlinear Optimization

Citation: NA\183, Department of Mathematics, University of Dundee, UK, August, 1998.

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Entry Submitted: 08/21/2000
Entry Last Modified: 05/25/2001

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