Résumé
| langue originale | Anglais |
|---|---|
| Pages (de - à) | 414-444 |
| Nombre de pages | 31 |
| journal | SIAM Journal on Optimization |
| Volume | 19 |
| Numéro de publication | 1 |
| Les DOIs | |
| état | Publié - 1 janv. 2008 |
Empreinte digitale
Citer ceci
}
Recursive trust-region methods for multiscale nonlinear optimization. / Gratton, Serge; Sartenaer, Annick; Toint, Philippe.
Dans: SIAM Journal on Optimization, Vol 19, Numéro 1, 01.01.2008, p. 414-444.Résultats de recherche: Contribution à un journal/une revue › Article
TY - JOUR
T1 - Recursive trust-region methods for multiscale nonlinear optimization
AU - Gratton, Serge
AU - Sartenaer, Annick
AU - Toint, Philippe
N1 - Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2008/1/1
Y1 - 2008/1/1
N2 - A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a means of speeding up the computation of the step. This use is recursive, leading to true multilevel/multiscale optimization methods reminiscent of multigrid methods in linear algebra and the solution of partial differential equations. A simple algorithm of the class is then described and its numerical performance is shown to be numerically promising. This observation then motivates a proof of global convergence to first-order stationary points on the fine grid that is valid for all algorithms in the class. © 2008 Society for Industrial and Applied Mathematics.
AB - A class of trust-region methods is presented for solving unconstrained nonlinear and possibly nonconvex discretized optimization problems, like those arising in systems governed by partial differential equations. The algorithms in this class make use of the discretization level as a means of speeding up the computation of the step. This use is recursive, leading to true multilevel/multiscale optimization methods reminiscent of multigrid methods in linear algebra and the solution of partial differential equations. A simple algorithm of the class is then described and its numerical performance is shown to be numerically promising. This observation then motivates a proof of global convergence to first-order stationary points on the fine grid that is valid for all algorithms in the class. © 2008 Society for Industrial and Applied Mathematics.
KW - nonlinear optimization
KW - recursive algorithms
KW - simplified models
KW - multilevel problems
KW - convergence theory
UR - http://www.scopus.com/inward/record.url?scp=61349175317&partnerID=8YFLogxK
U2 - 10.1137/050623012
DO - 10.1137/050623012
M3 - Article
VL - 19
SP - 414
EP - 444
JO - SIAM Journal on Optimization
JF - SIAM Journal on Optimization
SN - 1052-6234
IS - 1
ER -