Projets par an
Résumé
When solving the general smooth nonlinear and possibly nonconvex optimization problem involving equality and/or inequality constraints, an approximate first-order critical point of accuracy ∈ can be obtained by a second-order method using cubic regularization in at most O(∈<sup>-3/2</sup> ) evaluations of problem functions, the same order bound as in the unconstrained case. This result is obtained by first showing that the same result holds for inequality constrained nonlinear least-squares. As a consequence, the presence of (possibly nonconvex) equality/inequality constraints does not affect the complexity of finding approximate first-order critical points in nonconvex optimization. This result improves on the best known (O(∈<sup>-2</sup> )) evaluation-complexity bound for solving general nonconvexly constrained optimization problems.
langue originale | Anglais |
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Pages (de - à) | 836-851 |
Nombre de pages | 16 |
journal | SIAM Journal on Numerical Analysis |
Volume | 53 |
Numéro de publication | 2 |
Les DOIs | |
Etat de la publication | Publié - 2015 |
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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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A path and some adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Orateur)
24 oct. 2017Activité: Types de discours ou de présentation › Discours invité
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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