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
Full Text: