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

Serge Gratton; Vincent Malmedy; Philippe Toint

doi:10.1007/s10589-011-9393-3

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 language	English
Pages (from-to)	967-979
Number of pages	13
Journal	Computational Optimization and Applications
Volume	51
Issue number	3
DOIs	https://doi.org/10.1007/s10589-011-9393-3
Publication status	Published - 1 Apr 2012

Keywords

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

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10.1007/s10589-011-9393-3

Technical Report 18-2009Submitted manuscript, 269 KB

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ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization
SARTENAER, A. & TOINT, P.
1/01/87 → …
Project: Research Axis
Multiscale nonlinear optimization
SARTENAER, A., TOINT, P., Malmedy, V., Tomanos, D. & Weber Mendonca, M.
1/07/04 → 31/07/11
Project: Research

Cite this

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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. {\textcopyright} Springer Science+Business Media, LLC 2011.",

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

Abstract

Keywords

Access to Document

ADALGOPT: ADALGOPT - Advanced algorithms in nonlinear optimization

Multiscale nonlinear optimization

Cite this