Projets par an
Résumé
This paper examines worst-case evaluation bounds for finding weak minimizers in unconstrained optimization. For the cubic regularization algorithm, Nesterov and Polyak (2006) [15] and Cartis et al. (2010) [3] show that at most O(ε ) iterations may have to be performed for finding an iterate which is within of satisfying second-order optimality conditions. We first show that this bound can be derived for a version of the algorithm, which only uses one-dimensional global optimization of the cubic model and that it is sharp. We next consider the standard trust-region method and show that a bound of the same type may also be derived for this method, and that it is also sharp in some cases. We conclude by showing that a comparison of the bounds on the worst-case behaviour of the cubic regularization and trust-region algorithms favours the first of these methods. © 2011 Elsevier Inc. All rights reserved.
langue originale | Anglais |
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Pages (de - à) | 93-108 |
Nombre de pages | 16 |
journal | Journal of Complexity |
Volume | 28 |
Les DOIs | |
Etat de la publication | Publié - 1 févr. 2012 |
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Projets
- 2 Actif
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Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche
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ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
1/01/87 → …
Projet: Axe de recherche
Activités
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How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Orateur invité)
5 févr. 2016Activité: Types de discours ou de présentation › Présentation orale
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Polytechnic University of Hong Kong
Philippe Toint (Chercheur visiteur)
31 janv. 2016 → 14 févr. 2016Activité: Types de Visite d'une organisation externe › Recherche/Enseignement dans une institution externe
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How much patience do you have? Issues in complexity for nonlinear optimization
Philippe Toint (Orateur)
31 janv. 2016Activité: Types de discours ou de présentation › Présentation orale