Approximating Hessians in unconstrained optimization arising from discretized problems

V. Malmedy, Philippe Toint

Résultats de recherche: Contribution à un journal/une revueArticle

30 Downloads (Pure)

Résumé

We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finite-difference methods and updating schemes based on the secant equation are presented and compared numerically inside the multilevel trust-region algorithm proposed by Gratton et al. (IMA J. Numer. Anal. 28(4):827-861, 2008).
langue originaleAnglais
Pages (de - à)1-22
Nombre de pages22
journalComputational Optimization and Applications
Volume50
Numéro de publication1
Les DOIs
étatPublié - 1 sept. 2011

Empreinte digitale

Unconstrained Optimization
Newton-Raphson method
Finite difference method
Trust Region Algorithm
Large-scale Optimization
Quasi-Newton Method
Separability
Chord or secant line
Approximation Scheme
Sparsity
Difference Method
Updating
Finite Difference
Iteration
Partial
Context

Citer ceci

@article{204f09e180e54d27975f0cd1186a94e3,
title = "Approximating Hessians in unconstrained optimization arising from discretized problems",
abstract = "We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finite-difference methods and updating schemes based on the secant equation are presented and compared numerically inside the multilevel trust-region algorithm proposed by Gratton et al. (IMA J. Numer. Anal. 28(4):827-861, 2008).",
author = "V. Malmedy and Philippe Toint",
note = "Copyright 2011 Elsevier B.V., All rights reserved.",
year = "2011",
month = "9",
day = "1",
doi = "10.1007/s10589-010-9317-7",
language = "English",
volume = "50",
pages = "1--22",
journal = "Computational Optimization and Applications",
issn = "0926-6003",
publisher = "Springer Netherlands",
number = "1",

}

Approximating Hessians in unconstrained optimization arising from discretized problems. / Malmedy, V.; Toint, Philippe.

Dans: Computational Optimization and Applications, Vol 50, Numéro 1, 01.09.2011, p. 1-22.

Résultats de recherche: Contribution à un journal/une revueArticle

TY - JOUR

T1 - Approximating Hessians in unconstrained optimization arising from discretized problems

AU - Malmedy, V.

AU - Toint, Philippe

N1 - Copyright 2011 Elsevier B.V., All rights reserved.

PY - 2011/9/1

Y1 - 2011/9/1

N2 - We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finite-difference methods and updating schemes based on the secant equation are presented and compared numerically inside the multilevel trust-region algorithm proposed by Gratton et al. (IMA J. Numer. Anal. 28(4):827-861, 2008).

AB - We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finite-difference methods and updating schemes based on the secant equation are presented and compared numerically inside the multilevel trust-region algorithm proposed by Gratton et al. (IMA J. Numer. Anal. 28(4):827-861, 2008).

UR - http://www.scopus.com/inward/record.url?scp=79961006834&partnerID=8YFLogxK

U2 - 10.1007/s10589-010-9317-7

DO - 10.1007/s10589-010-9317-7

M3 - Article

AN - SCOPUS:79961006834

VL - 50

SP - 1

EP - 22

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

SN - 0926-6003

IS - 1

ER -