An interior-point ℓ1-penalty method for nonlinear optimization

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

Résultats de recherche: Contribution dans un livre/un catalogue/un rapport/dans les actes d'une conférenceChapitre (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.

langueAnglais
titreSpringer Proceedings in Mathematics and Statistics
Sous-titreProceedings of NAOIII 2014
EditeurSpringer New York
Pages117-150
Nombre de pages34
Volume134
ISBN (imprimé)9783319176888
Les DOIs
étatPublié - 2015
Evénement3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014 - Muscat, Oman
Durée: 5 janv. 20149 janv. 2014

Une conférence

Une conférence3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014
PaysOman
La villeMuscat
période5/01/149/01/14

Empreinte digitale

Penalty Method
Interior Point
Nonlinear Optimization
Penalty
Penalty Function
Multiplier
Exactness
Local Convergence
Certificate
Degeneracy
Nonlinear Programming
Trivial
Interior
Eliminate
Strictly
Infinity

mots-clés

    Citer ceci

    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
    Gould, Nick I M ; Orban, Dominique ; Toint, Philippe L. / An interior-point ℓ1-penalty method for nonlinear optimization. Springer Proceedings in Mathematics and Statistics: Proceedings of NAOIII 2014. Vol 134 Springer New York, 2015. p. 117-150
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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 conférenceChapitre (revu par des pairs)

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    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

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    Gould NIM, Orban D, Toint PL. 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. 2015. p. 117-150 https://doi.org/10.1007/978-3-319-17689-5_6