Using approximate secant equations in limited memory methods for multilevel unconstrained optimization

Serge Gratton, Vincent Malmedy, Philippe Toint

Research output: Contribution to journalArticle

30 Downloads (Pure)


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. © Springer Science+Business Media, LLC 2011.
Original languageEnglish
Pages (from-to)967-979
Number of pages13
JournalComputational Optimization and Applications
Issue number3
Publication statusPublished - 1 Apr 2012



  • nonlinear conjugate gradient methods
  • nonlinear optimization
  • quasi-Newton methods
  • multilevel problems
  • limited-memory algorithms

Cite this