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SUMMARY:Moment representations\, exactness and approximation.
DTSTART;VALUE=DATE-TIME:20211202T093000Z
DTEND;VALUE=DATE-TIME:20211202T103000Z
DTSTAMP;VALUE=DATE-TIME:20220523T151231Z
UID:indico-event-7025@indico.math.cnrs.fr
DESCRIPTION:How well is a measure characterized by its moments is an old q
uestion\nwhich appear in many contexts and applications. In polynomial\n
optimization\, it is the basis for so-called moment relaxation\nhierarchie
s\, which allow to compute global optima of polynomial\nfunctions on (comp
act) basic semi-algebraic sets. Computing the optimal\nmoment sequence(s)\
, positive on the quadratic module of the\nsemi-algebraic set\, by convex
optimization\, one can approximate the\nglobal solution(s) of the non-line
ar optimization problem.\n\nIn this talk\, we will discuss conditions for
which this approach gives\nan exact moment representation of a measure.
We will then consider the\nproperties of approximation of moment sequences
\, give an Effective\nPutinar Positivstellensatz and present a quantitativ
e analysis of the\napproximation of measures by positive moment sequences\
, with new\npolynomial bounds in the intrinsic parameters of the problem.
This\npresentation is based on a join work with Lorenzo Baldi.\n\nhttps://
indico.math.cnrs.fr/event/7025/
LOCATION:https://bbb.unilim.fr/b/vac-m6r-7dv
URL:https://indico.math.cnrs.fr/event/7025/
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