Sums of squares certificates for polynomial moment inequalities

Author name not available (Why is that?)

Publication date: 9 June 2023

Abstract: This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported on semialgebraic sets and subject to moment polynomial constraints is investigated. A positive solution to Hilbert's 17th problem for pseudo-moments is given. On the other hand, moment polynomials positive on actual measures are shown to be sums of squares and formal moments of squares up to arbitrarily small perturbation of their coefficients. When only measures supported on a bounded semialgebraic set are considered, a stronger algebraic certificate for moment polynomial positivity is derived. This result gives rise to a converging hierarchy of semidefinite programs for moment polynomial optimization. Finally, as an application, two nonlinear Bell inequalities from quantum physics are settled.

Has companion code repository: https://github.com/magronv/mompop

Mathematics Subject Classification ID

No records found.

This page was built for publication: Sums of squares certificates for polynomial moment inequalities

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6439757)