Inverse parametric convex programming problems via convex liftings

Abstract : The present paper introduces a procedure to recover an inverse parametric linear or quadratic programming problem from a given liftable polyhedral partition over which a continuous piecewise affine function is defined. The solution to the resulting parametric linear problem is exactly the initial piecewise affine function over the given original parameter space partition. We provide sufficient conditions for the existence of solutions for such inverse problems. Furthermore, the constructive procedure proposed here requires at most one supplementary variable in the vector of optimization arguments. The principle of this method builds upon an inverse map to the orthogonal projection, known as a convex lifting. Finally, we show that the theoretical results has a practical interest in Model Predictive Control (MPC) design. It is shown that any linear Model Predictive Controller can be obtained through a reformulated MPC problem with control horizon equal to two prediction steps.
Type de document :
Communication dans un congrès
19th World Congress of the International Federation of Automatic Control - IFAC 2014, Aug 2014, Cape Town, South Africa. Proceedings of the 19th World Congress of the International Federation of Automatic Control, 〈10.3182/20140824-6-ZA-1003.02364〉
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger

https://hal-supelec.archives-ouvertes.fr/hal-01086492
Contributeur : Pascale Lepeltier <>
Soumis le : vendredi 22 mai 2015 - 14:56:01
Dernière modification le : jeudi 29 mars 2018 - 11:06:05
Document(s) archivé(s) le : mardi 15 septembre 2015 - 06:43:20

Fichier

IFACWC14_vf.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Ngoc Anh Nguyen, Sorin Olaru, Pedro Rodriguez-Ayerbe, Morten Hovd, Ion Necoara. Inverse parametric convex programming problems via convex liftings. 19th World Congress of the International Federation of Automatic Control - IFAC 2014, Aug 2014, Cape Town, South Africa. Proceedings of the 19th World Congress of the International Federation of Automatic Control, 〈10.3182/20140824-6-ZA-1003.02364〉. 〈hal-01086492〉

Partager

Métriques

Consultations de la notice

255

Téléchargements de fichiers

100