English
The moment-LP and moment-SOS hierarchies
Post-edited
Auteurs : Lasserre, Jean Bernard (Auteur de la Conférence)
CIRM (Editeur )
44A60 - Moment problems
90C22 - Semidefinite programming
CIRM (Editeur )
Résumé :
We review basic properties of the moment-LP and moment-SOS hierarchies for polynomial optimization and compare them. We also illustrate how to use such a methodology in two applications outside optimization. Namely :
- for approximating (as claosely as desired in a strong sens) set defined with quantifiers of the form
$R_1 =\{ x\in B : f(x,y)\leq 0 $ for all $y$ such that $(x,y) \in K \}$.
$D_1 =\{ x\in B : f(x,y)\leq 0 $ for some $y$ such that $(x,y) \in K \}$.
by a hierarchy of inner sublevel set approximations
$\Theta_k = \left \{ x\in B : J_k(x)\leq 0 \right \}\subset R_f$.
or outer sublevel set approximations
$\Theta_k = \left \{ x\in B : J_k(x)\leq 0 \right \}\supset D_f$.
for some polynomiales $(J_k)$ of increasing degree :
- for computing convex polynomial underestimators of a given polynomial $f$ on a box $B \subset R^n$.
Codes MSC : - for approximating (as claosely as desired in a strong sens) set defined with quantifiers of the form
$R_1 =\{ x\in B : f(x,y)\leq 0 $ for all $y$ such that $(x,y) \in K \}$.
$D_1 =\{ x\in B : f(x,y)\leq 0 $ for some $y$ such that $(x,y) \in K \}$.
by a hierarchy of inner sublevel set approximations
$\Theta_k = \left \{ x\in B : J_k(x)\leq 0 \right \}\subset R_f$.
or outer sublevel set approximations
$\Theta_k = \left \{ x\in B : J_k(x)\leq 0 \right \}\supset D_f$.
for some polynomiales $(J_k)$ of increasing degree :
- for computing convex polynomial underestimators of a given polynomial $f$ on a box $B \subset R^n$.
44A60 - Moment problems
90C22 - Semidefinite programming
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 05/02/14 Date de captation : 12/11/13 Sous collection : Research talks arXiv category : Optimization and Control Domaine : Control Theory & Optimization Format : QuickTime (.mov) Durée : 00:53:12 Audience : Researchers Download : https://videos.cirm-math.fr/2013-11-12_Lasserre.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Geometry and algebra of linear matrix inequalities / Géométrie et algèbre des inégalités matricielles linéairesOrganisateurs de la rencontre : Banica, Valeria ; Laurent, Monique Dates : 12/11/13 - 15/11/13 Année de la rencontre : 2013 URL Congrès : http://homepages.laas.fr/henrion/geolmi13/
Données de citation
DOI : 10.24350/CIRM.V.18448603Citer cette vidéo: Lasserre, Jean Bernard (2013). The moment-LP and moment-SOS hierarchies. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18448603 URI : http://dx.doi.org/10.24350/CIRM.V.18448603 |
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