Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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D. Henrion - S. Naldi - M. Safey El Din

Algebraic certificates for the truncated moment problem

created by naldi on 20 Jul 2023



Inserted: 20 jul 2023
Last Updated: 20 jul 2023

Year: 2023

ArXiv: 2302.06927 PDF


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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