Any Discontinuous PWA Function Is Optimal Solution to a Parametric Linear Programming Problem

Ngoc Anh Nguyen 1, 2 Pedro Rodriguez-Ayerbe 1 Sorin Olaru 1, 3
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : Recent studies have investigated the continuous functions in terms of inverse optimality. The continuity is a primordial structural property which is exploited in order to link a given piecewise affine (PWA) function to an optimization problem. The aim of this work is to deepen the study of the PWA functions in the inverse optimality context and specifically deal with the presence of discontinuities. First, it will be shown that a solution to the inverse optimality problem exists via a constructive argument. The loss of continuity will have an implication on the structure of the optimization problem which, albeit convex, turns to have a set-valued optimal solution. As a consequence, the original PWA function will represent an optimal solution but the uniqueness is lost. From the numerical point of view, we introduce an algorithm to construct an optimization problem that admits a given discontinuous PWA unction as an optimal solution. This construction is shown to rely on convex liftings. A numerical example is considered to illustrate the proposal.
Type de document :
Pré-publication, Document de travail
Liste complète des métadonnées

Littérature citée [19 références]  Voir  Masquer  Télécharger
Contributeur : Pascale Lepeltier <>
Soumis le : lundi 20 juin 2016 - 13:11:16
Dernière modification le : mardi 17 avril 2018 - 09:08:49
Document(s) archivé(s) le : jeudi 22 septembre 2016 - 21:15:33


IPLQP discontinuous PWA.pdf
Fichiers produits par l'(les) auteur(s)


  • HAL Id : hal-01259879, version 1


Ngoc Anh Nguyen, Pedro Rodriguez-Ayerbe, Sorin Olaru. Any Discontinuous PWA Function Is Optimal Solution to a Parametric Linear Programming Problem. 2016. 〈hal-01259879〉



Consultations de la notice


Téléchargements de fichiers