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Article Dans Une Revue Optimization Letters Année : 2015

Volume of slices and sections of the simplex in closed form

Résumé

Given a vector a ∈ Rn , we provide an alternative and direct proof for the formula of the volume of sections ∆ ∩ {x : a T x <= t} and slices ∆ ∩ {x : a T x = t}, t ∈ R, of the simplex ∆. For slices the formula has already been derived but as a by-product of the construction of univariate B-Splines. One goal of the paper is to also show how simple and powerful can be the Laplace transform technique to derive closed form expression for some multivariate integrals. It also complements some previous results obtained for the hypercube [0, 1] n .
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Dates et versions

hal-01095071 , version 1 (15-12-2014)

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Jean-Bernard Lasserre. Volume of slices and sections of the simplex in closed form. Optimization Letters, 2015, 9 (7), pp.1263--1269. ⟨hal-01095071⟩
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