@Article{JCM-24-676,
author = {Serge Gratton, Annick Sartenaer and Philippe L. Toint},
title = {Second-Order Convergence Properties of Trust-Region Methods Using Incomplete Curvature Information, with an Application to Multigrid Optimization},
journal = {Journal of Computational Mathematics},
year = {2006},
volume = {24},
number = {6},
pages = {676--692},
abstract = {<p style="text-align: justify;">Convergence properties of trust-region methods for unconstrained nonconvex optimization is considered in the case where information on the objective function&#39;s local curvature is incomplete, in the sense that it may be restricted to a fixed set of &quot;test directions&quot; and may not be available at every iteration. It is shown that convergence to local &quot;weak&quot; 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. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/8783.html}
}