@article{9b6209cc259248218f4210fef2b6a227,
title = "Using approximate secant equations in limited memory methods for multilevel unconstrained optimization",
abstract = "The properties of multilevel optimization problems defined on a hierarchy of discretization grids can be used to define approximate secant equations, which describe the second-order behavior of the objective function. Following earlier work by Gratton and Toint (2009) we introduce a quasi-Newton method (with a linesearch) and a nonlinear conjugate gradient method that both take advantage of this new second-order information. We then present numerical experiments with these methods and formulate recommendations for their practical use. {\textcopyright} Springer Science+Business Media, LLC 2011.",
keywords = " nonlinear conjugate gradient methods, nonlinear optimization, quasi-Newton methods, multilevel problems, limited-memory algorithms",
author = "Serge Gratton and Vincent Malmedy and Philippe Toint",
note = "Copyright 2012 Elsevier B.V., All rights reserved.",
year = "2012",
month = apr,
day = "1",
doi = "10.1007/s10589-011-9393-3",
language = "English",
volume = "51",
pages = "967--979",
journal = "Computational Optimization and Applications",
publisher = "Springer Netherlands",
number = "3",
}