An interior-point ℓ1-penalty method for nonlinear optimization

Nick I M Gould; Dominique Orban; Philippe L. Toint

doi:10.1007/978-3-319-17689-5_6

An interior-point ℓ₁-penalty method for nonlinear optimization

Nick I M Gould, Dominique Orban, Philippe L. Toint

Namur Institute for Complex Systems

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Chapitre (revu par des pairs)

Résumé

We describe a mixed interior/exterior-point method for nonlinear programming that handles constraints by way of an ℓ₁-penalty function. The penalty problem is reformulated as a smooth inequality-constrained problem that always possesses bounded multipliers, and that may be solved using interior-point techniques as finding a strictly feasible point is trivial. If finite multipliers exist for the original problem, exactness of the penalty function eliminates the need to drive the penalty parameter to infinity. If the penalty parameter needs to increase without bound and if feasibility is ultimately attained, a certificate of degeneracy is delivered. Global and fast local convergence of the proposed scheme are established and practical aspects of the method are discussed.

langue originale	Anglais
titre	Springer Proceedings in Mathematics and Statistics
Sous-titre	Proceedings of NAOIII 2014
Editeur	Springer New York
Pages	117-150
Nombre de pages	34
Volume	134
ISBN (imprimé)	9783319176888
Les DOIs	https://doi.org/10.1007/978-3-319-17689-5_6
Etat de la publication	Publié - 2015
Evénement	3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014 - Muscat, Oman Durée: 5 janv. 2014 → 9 janv. 2014

Une conférence

Une conférence	3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014
Pays	Oman
La ville	Muscat
période	5/01/14 → 9/01/14

Accès au document

10.1007/978-3-319-17689-5_6

Link to publication in Scopus

Empreinte digitale Examiner les sujets de recherche de « An interior-point ℓ<sub>1</sub>-penalty method for nonlinear optimization ». Ensemble, ils forment une empreinte digitale unique.

Projets

2 Actif

GALAHAD: GALAHAD, une collection de logiciels pour l'optimisation non linéaire

TOINT, P.

1/03/00 → …

Projet: Recherche

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

SARTENAER, A. & TOINT, P.

1/01/87 → …

Projet: Axe de recherche

Contient cette citation

Gould, N. I. M., Orban, D., & Toint, P. L. (2015). An interior-point ℓ₁-penalty method for nonlinear optimization. Dans Springer Proceedings in Mathematics and Statistics: Proceedings of NAOIII 2014 (Vol 134, p. 117-150). Springer New York. https://doi.org/10.1007/978-3-319-17689-5_6

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title = "An interior-point ℓ1-penalty method for nonlinear optimization",

abstract = "We describe a mixed interior/exterior-point method for nonlinear programming that handles constraints by way of an ℓ1-penalty function. The penalty problem is reformulated as a smooth inequality-constrained problem that always possesses bounded multipliers, and that may be solved using interior-point techniques as finding a strictly feasible point is trivial. If finite multipliers exist for the original problem, exactness of the penalty function eliminates the need to drive the penalty parameter to infinity. If the penalty parameter needs to increase without bound and if feasibility is ultimately attained, a certificate of degeneracy is delivered. Global and fast local convergence of the proposed scheme are established and practical aspects of the method are discussed.",

keywords = "Elastic variables, Interior point, Nonconvex Optimization, ℓ-Penalty",

author = "Gould, {Nick I M} and Dominique Orban and Toint, {Philippe L.}",

year = "2015",

doi = "10.1007/978-3-319-17689-5_6",

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booktitle = "Springer Proceedings in Mathematics and Statistics",

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Gould, NIM, Orban, D & Toint, PL 2015, An interior-point ℓ₁-penalty method for nonlinear optimization. Dans Springer Proceedings in Mathematics and Statistics: Proceedings of NAOIII 2014. VOL. 134, Springer New York, p. 117-150, 3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014, Muscat, Oman, 5/01/14. https://doi.org/10.1007/978-3-319-17689-5_6

An interior-point ℓ₁-penalty method for nonlinear optimization. / Gould, Nick I M; Orban, Dominique; Toint, Philippe L.

Springer Proceedings in Mathematics and Statistics: Proceedings of NAOIII 2014. Vol 134 Springer New York, 2015. p. 117-150.

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférence › Chapitre (revu par des pairs)

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AU - Gould, Nick I M

AU - Orban, Dominique

AU - Toint, Philippe L.

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N2 - We describe a mixed interior/exterior-point method for nonlinear programming that handles constraints by way of an ℓ1-penalty function. The penalty problem is reformulated as a smooth inequality-constrained problem that always possesses bounded multipliers, and that may be solved using interior-point techniques as finding a strictly feasible point is trivial. If finite multipliers exist for the original problem, exactness of the penalty function eliminates the need to drive the penalty parameter to infinity. If the penalty parameter needs to increase without bound and if feasibility is ultimately attained, a certificate of degeneracy is delivered. Global and fast local convergence of the proposed scheme are established and practical aspects of the method are discussed.

AB - We describe a mixed interior/exterior-point method for nonlinear programming that handles constraints by way of an ℓ1-penalty function. The penalty problem is reformulated as a smooth inequality-constrained problem that always possesses bounded multipliers, and that may be solved using interior-point techniques as finding a strictly feasible point is trivial. If finite multipliers exist for the original problem, exactness of the penalty function eliminates the need to drive the penalty parameter to infinity. If the penalty parameter needs to increase without bound and if feasibility is ultimately attained, a certificate of degeneracy is delivered. Global and fast local convergence of the proposed scheme are established and practical aspects of the method are discussed.

KW - Elastic variables

KW - Interior point

KW - Nonconvex Optimization

KW - ℓ-Penalty

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