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Pré-Publication, Document De Travail Année : 2008

Approximate volume and integration for basic semi-algebraic sets

Résumé

Given a basic compact semi-algebraic set $K$ in $R^n$ we introduce a methodology that provides a sequence converging to the volume of $K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear programs. Not only the volume but also every finite vector of moments of the probability measure uniformly distributed on $K$ can be approximated as closely as desired, and so permits to approximate the integral on $K$ of any given polynomial; extension to integration against some weight functions is also provided. Finally, some numerical aspects are discussed.
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Dates et versions

hal-00297384 , version 1 (16-07-2008)
hal-00297384 , version 2 (31-08-2009)

Identifiants

Citer

Didier Henrion, Jean-Bernard Lasserre, Carlo Savorgnan. Approximate volume and integration for basic semi-algebraic sets. 2008. ⟨hal-00297384v1⟩

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