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 
@article{RO_2009__43_3_309_0,
     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://archive.numdam.org/articles/10.1051/ro/2009016/}
}
TY  - JOUR
AU  - Sainvitu, Caroline
TI  - How much do approximate derivatives hurt filter methods ?
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2009
SP  - 309
EP  - 329
VL  - 43
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ro/2009016/
DO  - 10.1051/ro/2009016
LA  - en
ID  - RO_2009__43_3_309_0
ER  - 
%0 Journal Article
%A Sainvitu, Caroline
%T How much do approximate derivatives hurt filter methods ?
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2009
%P 309-329
%V 43
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ro/2009016/
%R 10.1051/ro/2009016
%G en
%F RO_2009__43_3_309_0
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://archive.numdam.org/articles/10.1051/ro/2009016/

[1] R.H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16 (1995) 1190-1208. | MR | Zbl

[2] A.R. Conn, N.I.M. Gould and P.L. Toint, Convergence of quasi-Newton matrices generated by the Symmetric Rank One update. Math. Program. 50 (1991) 177-196. | MR | Zbl

[3] A.R. Conn, N.I.M. Gould and P.L. Toint, Trust-Region Methods. MPS-SIAM Series on Optimization 1, SIAM, Philadelphia, USA (2000). | MR | Zbl

[4] A.R. Conn, K. Scheinberg and P.L. Toint, Recent progress in unconstrained nonlinear optimization without derivatives. Math. Program. Ser. B 79 (1997) 397-414. | MR | Zbl

[5] E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201-213. | MR | Zbl

[6] R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function. Math. Program. 91 (2002) 239-269. | MR | Zbl

[7] N.I.M. Gould, S. Leyffer and P.L. Toint, A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. SIAM J. Optim. 15 (2005) 17-38. | MR | Zbl

[8] N.I.M. Gould, S. Lucidi, M. Roma and P.L. Toint, Solving the trust-region subproblem using the Lanczos method. SIAM J. Optim. 9 (1999) 504-525. | MR | Zbl

[9] N.I.M. Gould, D. Orban, A. Sartenaer and P.L. Toint, Sensitivity of trust-region algorithms on their parameters. 4OR, Quarterly Journal of Operations Research 3 (2005) 227-241. | MR | Zbl

[10] N.I.M. Gould, D. Orban and P.L. Toint, CUTEr, a constrained and unconstrained testing environment, revisited ACM Trans. Math. Software 29 (2003) 373-394. | MR | Zbl

[11] N.I.M. Gould, D. Orban and P.L. Toint, GALAHAD - a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Software 29 (2003) 353-372. | MR | Zbl

[12] N.I.M. Gould, C. Sainvitu and P.L. Toint, A Filter-Trust-Region Method for Unconstrained Optimization. SIAM J. Optim. 16 (2005) 341-357. | MR | Zbl

[13] N.I.M. Gould and P.L. Toint, FILTRANE, a Fortran 95 Filter-Trust-Region Package for Solving Systems of Nonlinear Equalities, Nonlinear Inequalities and Nonlinear Least-Squares Problems. Technical report 03/15, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK (2003).

[14] D.C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization. Math. Program. Ser. B 45 (1989) 503-528. | MR | Zbl

[15] D.F. Shanno and K.H. Phua, Matrix conditionning and nonlinear optimization. Math. Program. 14 (1978) 149-160. | MR | Zbl

Cité par Sources :