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Preprints, Working Papers, ... Year : 2023

Algebraic certificates for the truncated moment problem

Abstract

The truncated moment problem consists of determining whether a given finitedimensional vector of real numbers y is obtained by integrating a basis of the vector space of polynomials of bounded degree with respect to a non-negative measure on a given set K of a finite-dimensional Euclidean space. This problem has plenty of applications e.g. in optimization, control theory and statistics. When K is a compact semialgebraic set, the duality between the cone of moments of non-negative measures on K and the cone of non-negative polynomials on K yields an alternative: either y is a moment vector, or y is not a moment vector, in which case there exists a polynomial strictly positive on K making a linear functional depending on y vanish. Such a polynomial is an algebraic certificate of moment unrepresentability. We study the complexity of computing such a certificate using computer algebra algorithms.
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hal-03987123 , version 1 (13-02-2023)

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Didier Henrion, Simone Naldi, Mohab Safey El Din. Algebraic certificates for the truncated moment problem. 2023. ⟨hal-03987123⟩
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