How much do approximate derivatives hurt filter methods ?
RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 3, pp. 309-329.

Dans ce papier, nous examinons l'influence des dérivées premières et secondes approximées sur l'algorithme de filtre de type région de confiance développé pour résoudre des problèmes d'optimisa-tion non-linéaire sans contraintes et proposé par Gould, Sainvitu et Toint dans [12]. Des résultats numériques effectués sur un ensemble de problèmes de petite taille provenant de la collection CUTEr décrivent l'effet de l'utilisation de dérivées approximées sur la robustesse et l'effi-cacité de la méthode de filtre de type région de confiance.

In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.

DOI : 10.1051/ro/2009016
Classification : 65K05, 90C26, 90C30, 90C53
Keywords: unconstrained optimization, filter techniques, trust-region algorithms, approximate derivatives, numerical results
Mots-clés : optimisation sans contraintes, méthode de filtre, algorithme de type de région de confiance, dérivées approximées, résultats numériques 
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     author = {Sainvitu, Caroline},
     title = {How much do approximate derivatives hurt filter methods ?},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {309--329},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {3},
     year = {2009},
     doi = {10.1051/ro/2009016},
     mrnumber = {2567991},
     zbl = {1175.65074},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2009016/}
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Sainvitu, Caroline. How much do approximate derivatives hurt filter methods ?. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 3, pp. 309-329. doi : 10.1051/ro/2009016. http://www.numdam.org/articles/10.1051/ro/2009016/

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