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Bounds on measures satisfying moment conditions. (English) Zbl 1073.90534

Summary: Given a semialgebraic set \(S\subset \mathbb R^n\), we provide a numerical approximation procedure that provides upper and lower bounds on \(\mu(S)\), for measures \(\mu\) that satisfy some given moment conditions. The bounds are obtained as solutions of positive semidefinite programs that can be solved via standard software packages.

MSC:

90C22 Semidefinite programming
60D05 Geometric probability and stochastic geometry
90B22 Queues and service in operations research
90C25 Convex programming
28A75 Length, area, volume, other geometric measure theory
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