D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS - Archive ouverte HAL Access content directly
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D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS

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Abstract

We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial.
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Dates and versions

hal-01483490 , version 1 (06-03-2017)
hal-01483490 , version 2 (17-10-2017)

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Yohann de Castro, F Gamboa, Didier Henrion, Roxana Hess, Jean-Bernard Lasserre. D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS. 2017. ⟨hal-01483490v1⟩
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