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 | 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 | |
| état | 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 |
Empreinte digitale
mots-clés
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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)
TY - CHAP
T1 - An interior-point ℓ1-penalty method for nonlinear optimization
AU - Gould, Nick I M
AU - Orban, Dominique
AU - Toint, Philippe L.
PY - 2015
Y1 - 2015
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
UR - http://www.scopus.com/inward/record.url?scp=84947069317&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-17689-5_6
DO - 10.1007/978-3-319-17689-5_6
M3 - Chapter (peer-reviewed)
SN - 9783319176888
VL - 134
SP - 117
EP - 150
BT - Springer Proceedings in Mathematics and Statistics
PB - Springer New York
ER -