### Résumé

langue originale | Anglais |
---|---|

Pages (de - à) | 3512-3532 |

Nombre de pages | 21 |

journal | SIAM Journal on Optimization |

Volume | 20 |

Numéro de publication | 6 |

Les DOIs | |

état | Publié - 1 janv. 2010 |

### Empreinte digitale

### Citer ceci

*SIAM Journal on Optimization*,

*20*(6), 3512-3532. https://doi.org/10.1137/090748536

}

*SIAM Journal on Optimization*, VOL. 20, Numéro 6, p. 3512-3532. https://doi.org/10.1137/090748536

**Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization.** / Scheinberg, K.; Toint, Philippe.

Résultats de recherche: Contribution à un journal/une revue › Article

TY - JOUR

T1 - Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization

AU - Scheinberg, K.

AU - Toint, Philippe

N1 - Publication code : FP SB010/2009/06 ; QA 0002.2/001/09/06

PY - 2010/1/1

Y1 - 2010/1/1

N2 - Several efficient methods for derivative-free optimization are based on the construction and maintenance of an interpolation model for the objective function. Most of these algorithms use special "geometry-improving" iterations, where the geometry (poisedness) of the underlying interpolation set is made better at the cost of one or more function evaluations. We show that such geometry improvements cannot be completely eliminated if one wishes to ensure global convergence, but we also provide an algorithm where such steps occur only in the final stage of the algorithm, where criticality of a putative stationary point is verified. Global convergence for this method is proved by making use of a self-correction mechanism inherent to the combination of trust regions and interpolation models. This mechanism also throws some light on the surprisingly good numerical results reported by Fasano, Morales, and Nocedal [Optim. Methods Softw., 24 (2009), pp. 145-154] for a method where no care is ever taken to guarantee poisedness of the interpolation set. © 2010 Society for Industrial and Applied Mathematics.

AB - Several efficient methods for derivative-free optimization are based on the construction and maintenance of an interpolation model for the objective function. Most of these algorithms use special "geometry-improving" iterations, where the geometry (poisedness) of the underlying interpolation set is made better at the cost of one or more function evaluations. We show that such geometry improvements cannot be completely eliminated if one wishes to ensure global convergence, but we also provide an algorithm where such steps occur only in the final stage of the algorithm, where criticality of a putative stationary point is verified. Global convergence for this method is proved by making use of a self-correction mechanism inherent to the combination of trust regions and interpolation models. This mechanism also throws some light on the surprisingly good numerical results reported by Fasano, Morales, and Nocedal [Optim. Methods Softw., 24 (2009), pp. 145-154] for a method where no care is ever taken to guarantee poisedness of the interpolation set. © 2010 Society for Industrial and Applied Mathematics.

KW - derivative-free optimization

KW - geometry of the interpolation set

KW - unconstrained minimization

UR - http://www.scopus.com/inward/record.url?scp=79251516126&partnerID=8YFLogxK

U2 - 10.1137/090748536

DO - 10.1137/090748536

M3 - Article

VL - 20

SP - 3512

EP - 3532

JO - SIAM Journal on Optimization

JF - SIAM Journal on Optimization

SN - 1052-6234

IS - 6

ER -