Dual optimal design and the Christoffel–Darboux polynomial

Yohann De Castro; Fabrice Gamboa; Didier Henrion; Jean Bernard Lasserre

doi:10.1007/s11590-020-01680-2

Dual optimal design and the Christoffel–Darboux polynomial

Yohann De Castro
, Fabrice Gamboa
, Didier Henrion
, Jean Bernard Lasserre

Institut Camille Jordan
Université de Toulouse
Université Paul Sabatier
Faculty of Electrical Engineering

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

The purpose of this short note is to show that the Christoffel–Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. Geometric interpretations and algorithmic consequences are mentioned.

langue originale	Anglais
Pages (de - à)	3-8
Nombre de pages	6
journal	Optimization Letters
Volume	15
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s11590-020-01680-2
état	Publié - 1 févr. 2021
Modification externe	Oui

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10.1007/s11590-020-01680-2

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title = "Dual optimal design and the Christoffel–Darboux polynomial",

abstract = "The purpose of this short note is to show that the Christoffel–Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. Geometric interpretations and algorithmic consequences are mentioned.",

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AU - Henrion, Didier

AU - Lasserre, Jean Bernard

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AB - The purpose of this short note is to show that the Christoffel–Darboux polynomial, useful in approximation theory and data science, arises naturally when deriving the dual to the problem of semi-algebraic D-optimal experimental design in statistics. It uses only elementary notions of convex analysis. Geometric interpretations and algorithmic consequences are mentioned.

KW - Convex analysis

KW - Data science

KW - Semidefinite programming

KW - Statistics

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Dual optimal design and the Christoffel–Darboux polynomial

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