Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets

CTU); Didier Henrion (LAAS-MAC; Milan Korda

Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets

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arxiv 1612.04146 v1 pith:OGTN53TK submitted 2016-12-13 math.OC

Milan Korda , Didier Henrion (LAAS-MAC , CTU) This is my paper · ORCID

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keywords convergencevolumehierarchiesmoment-sum-of-squarespolynomialssemialgebraicsequenceabove

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Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set K. The idea consists of approximating from above the indicator function of K with a sequence of polynomials of increasing degree d, so that the integrals of these polynomials generate a convergence sequence of upper bounds on the volume of K. We show that the asymptotic rate of this convergence is at least O(1/ log log d).

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Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra
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Explicit convergence rates for noncommutative SOS hierarchies on the Pauli algebra are bounded using smallest roots of Krawtchouk polynomials.

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