Projets par an
Résumé
The evaluation complexity of general nonlinear, possibly nonconvex,
constrained optimization is analyzed. It is shown that, under suitable
smoothness conditions, an $\epsilon$-approximate first-order critical
point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, and
Toint (2011, 2013). It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the $\epsilon$-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers.
constrained optimization is analyzed. It is shown that, under suitable
smoothness conditions, an $\epsilon$-approximate first-order critical
point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's function and their first $p$ derivatives. This is achieved by using a two-phases algorithm inspired by Cartis, Gould, and
Toint (2011, 2013). It is also shown that strong guarantees (in terms of handling degeneracies) on the possible limit points of the sequence of iterates generated by this algorithm can be obtained at the cost of increased complexity. At variance with previous results, the $\epsilon$-approximate first-order criticality is defined by satisfying a version of the KKT conditions with an accuracy that does not depend on the size of the Lagrange multipliers.
| langue originale | Anglais |
|---|---|
| Nombre de pages | 20 |
| journal | SIAM Journal on Optimization |
| Volume | 26 |
| Numéro de publication | 2 |
| Etat de la publication | Publié - 2016 |
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Projets
- 2 Actif
Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche
ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
1/01/87 → …
Projet: Axe de recherche
Activités
A path and some adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Orateur)
23 oct. 2017
Activité: Types de discours ou de présentation › Discours invité
A path and some adventures in the jungle of high-order nonlinear optimization
Philippe Toint (Orateur)
24 oct. 2017
Activité: Types de discours ou de présentation › Discours invité
High-order optimality conditions in nonlinear optimization: necessary conditions and a conceptual approach of evaluation complexity
Philippe Toint (Orateur)
10 août 2016
Activité: Types de discours ou de présentation › Discours invité
Contient cette citation
Birgin, E., Gardenghi, J., Martinez, J-M., Santos, S., & Toint, P. (2016). Evaluation complexity for nonlinear constrained optimization using unscaled KKT conditions and high-order models. SIAM Journal on Optimization, 26(2).