COERCIVITY OF THE COMPUTATION OF SUM OF SQUARES FROM DATA POINTS: THE CASE OF THE HYPERCUBE - Sorbonne Université Access content directly
Preprints, Working Papers, ... Year : 2023

COERCIVITY OF THE COMPUTATION OF SUM OF SQUARES FROM DATA POINTS: THE CASE OF THE HYPERCUBE

Abstract

The goal of this work is to provide a simple condition on a multivariate polynomial p such that the convex dual function defined in a previous work [5] is coercive (infinite at infinity). It is based on the fact that data points obtained from tensorization of the roots of the third and fourth kind Chebyshev polynomials possess a strong stability property, so they are (nearly) optimal. The stability property is fundamentally connecte to the Lebesgue stability constant of Chebyshev interpolation. It has the consequence that G has a global minimum, which justifies on the hypercube the gradient descent algorithms proposed in [5]. A corollary is a constructive representation of p as a sum of squares (SOS) endowed with the Schmüdgen's Positivstellensatz structure.
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Dates and versions

hal-04034482 , version 1 (17-03-2023)

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  • HAL Id : hal-04034482 , version 1

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Bruno Despr És. COERCIVITY OF THE COMPUTATION OF SUM OF SQUARES FROM DATA POINTS: THE CASE OF THE HYPERCUBE: SUM OF SQUARES AND DATA POINTS. 2023. ⟨hal-04034482⟩
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