Approximate volume and integration for basic semi-algebraic sets - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue SIAM Review Année : 2009

Approximate volume and integration for basic semi-algebraic sets

Résumé

Given a basic compact semi-algebraic set $\K\subset\R^n$, we introduce a methodology that generates a sequence converging to the volume of $\K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear programs. Not only the volume but also every finite vector of moments of the probability measure that is uniformly distributed on $\K$ can be approximated as closely as desired, and so permits to approximate the integral on $\K$ of any given polynomial; extension to integration against some weight functions is also provided. Finally, some numerical issues associated with the algorithms involved are briefly discussed.
Fichier principal
Vignette du fichier
volume.pdf (441.76 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00297384 , version 1 (16-07-2008)
hal-00297384 , version 2 (31-08-2009)

Identifiants

Citer

Didier Henrion, Jean-Bernard Lasserre, Carlo Savorgnan. Approximate volume and integration for basic semi-algebraic sets. SIAM Review, 2009, 51 (4), pp.722-743. ⟨hal-00297384v2⟩
176 Consultations
240 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More