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The moment-LP and moment-SOS hierarchies
Post-edited
Authors : Lasserre, Jean Bernard (Author of the conference)
CIRM (Publisher )
44A60 - Moment problems
90C22 - Semidefinite programming
CIRM (Publisher )
Abstract :
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 $B \subset R^n$.
MSC Codes : - 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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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 05/02/14 Conference Date : 12/11/13 Subseries : Research talks arXiv category : Optimization and Control Mathematical Area(s) : Control Theory & Optimization Format : QuickTime (.mov) Video Time : 00:53:12 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2013-11-12_Lasserre.mp4 
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Information on the Event
Event Title : Geometry and algebra of linear matrix inequalities / Géométrie et algèbre des inégalités matricielles linéairesEvent Organizers : Banica, Valeria ; Laurent, Monique Dates : 12/11/13 - 15/11/13 Event Year : 2013 Event URL : http://homepages.laas.fr/henrion/geolmi13/
Citation Data
DOI : 10.24350/CIRM.V.18448603Cite 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 |
Bibliography
