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Post-edited The moment-LP and moment-SOS hierarchies

Auteurs : Lasserre, Jean Bernard (Auteur de la Conférence)
CIRM (Editeur )

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semidefinite programming why polynomial optimization SOS-based positivity certificate LP-based positivity certificate the moment-LP and moment-SOS approaches properties of the SOS hierarchy aproximation of sets with quantifiers polynomial matrix inequalities convex understimators of polynomials conclusion

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 :
44A60 - Moment problems
90C22 - Semidefinite programming

    Informations sur la Vidéo

    Réalisateur : Hennenfent, Guillaume
    Langue : Anglais
    Date de publication : 05/02/14
    Date de captation : 12/11/13
    Collection : Research talks
    Format : QuickTime (.mov) Durée : 00:53:12
    Domaine : Control Theory & Optimization
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : http://videos.cirm-math.fr/2013-11-12_Lasserre.mp4

Informations sur la rencontre

Nom du congrès : Geometry and algebra of linear matrix inequalities / Géométrie et algèbre des inégalités matricielles linéaires
Organisteurs Congrès : Banica, Valeria ; Laurent, Monique
Dates : 12/11/13 - 15/11/13
Année de la rencontre : 2013
URL Congrès : http://homepages.laas.fr/henrion/geolmi13/

Citation Data

DOI : 10.24350/CIRM.V.18448603
Cite this video as: 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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