Projets par an
Résumé
The adaptive cubic regularization algorithm described in Cartis et al. (2009, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program., 127, 245-295; 2010, Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function- and derivative-evaluation complexity [online]. Math. Program., DOI: 10.1007/s10107-009-0337-y) is adapted to the problem of minimizing a nonlinear, possibly nonconvex, smooth objective function over a convex domain. Convergence to first-order critical points is shown under standard assumptions, without any Lipschitz continuity requirement on the objective's Hessian. A worst-case complexity analysis in terms of evaluations of the problem's function and derivatives is also presented for the Lipschitz continuous case and for a variant of the resulting algorithm. This analysis extends the best-known bound for general unconstrained problems to nonlinear problems with convex constraints. © 2012 Crown copyright 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
langue originale | Anglais |
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Pages (de - à) | 1662-1695 |
Nombre de pages | 34 |
journal | IMA Journal of Numerical Analysis |
Volume | 32 |
Numéro de publication | 4 |
Les DOIs | |
Etat de la publication | Publié - 1 oct. 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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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
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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