Séminaire Calcul Formel
# Moment representations, exactness and approximation.

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by

→
Europe/Paris

https://bbb.unilim.fr/b/vac-m6r-7dv
#### https://bbb.unilim.fr/b/vac-m6r-7dv

Description

How well is a measure characterized by its moments is an old question

which appear in many contexts and applications. In polynomial

optimization, it is the basis for so-called moment relaxation

hierarchies, which allow to compute global optima of polynomial

functions on (compact) basic semi-algebraic sets. Computing the optimal

moment sequence(s), positive on the quadratic module of the

semi-algebraic set, by convex optimization, one can approximate the

global solution(s) of the non-linear optimization problem.

In this talk, we will discuss conditions for which this approach gives

an exact moment representation of a measure. We will then consider the

properties of approximation of moment sequences, give an Effective

Putinar Positivstellensatz and present a quantitative analysis of the

approximation of measures by positive moment sequences, with new

polynomial bounds in the intrinsic parameters of the problem. This

presentation is based on a join work with Lorenzo Baldi.