Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function's local curvature is incomplete, in the sense that it may be restricted to a fixed set of ``test directions'' and may not be available at every iteration. It is shown that convergence to local ``weak'' minimizers can still be obtained under some additional but algorithmically realistic conditions. These theoretical results are then applied to recursive multigrid trust-region methods, which suggests a new class of algorithms with guaranteed second-order convergence properties.
Report 05/8 Department of Mathematics, University of Namur, Namur, Belgium
View Second-order convergence properties of trust-region methods using incomplete curvature information, with an application to multigrid optimization