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

Serge Gratton, Vincent Malmedy, Philippe Toint

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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. © Springer Science+Business Media, LLC 2011.
Original languageEnglish
Pages (from-to)967-979
Number of pages13
JournalComputational Optimization and Applications
Volume51
Issue number3
DOIs
Publication statusPublished - 1 Apr 2012

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Keywords

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

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