Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization
Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 6 : pp. 676–692
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8783
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 6 : pp. 676–692
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Nonlinear optimization Convergence to local minimizers Multilevel problems.