Projets par an
Résumé
We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmoothness of the objective in that a first-order trust-region or quadratic regularization method applied to it takes at most O(ε-2) function evaluations to reduce the size of a first-order criticality measure below ε. Specializing this result to the case when the composite objective is an exact penalty function allows us to consider the objective- and constraintevaluation worst-case complexity of nonconvex equality-constrained optimization when the solution is computed using a first-order exact penalty method. We obtain that in the reasonable case when the penalty parameters are bounded, the complexity of reaching within ε of a KKT point is at most O(ε-2) problem evaluations, which is the same in order as the function-evaluation complexity of steepest-descent methods applied to unconstrained, nonconvex smooth optimization. © 2011 Society for Industrial and Applied Mathematics.
langue originale | Anglais |
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Pages (de - à) | 1721-1739 |
Nombre de pages | 19 |
journal | SIAM Journal on Optimization |
Volume | 21 |
Numéro de publication | 4 |
Les DOIs | |
Etat de la publication | Publié - 1 janv. 2011 |
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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