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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 |
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Pages (from-to) | 967-979 |
Number of pages | 13 |
Journal | Computational Optimization and Applications |
Volume | 51 |
Issue number | 3 |
DOIs | |
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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Projects
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Multiscale nonlinear optimization
SARTENAER, A., TOINT, P., Malmedy, V., Tomanos, D. & Weber Mendonca, M.
1/07/04 → 31/07/11
Project: Research