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Milan Korda(milan.kordaengineering.ucsb.edu) Abstract: Momentsumofsquares 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 $O(1 / \log \log d)$. Keywords: moment relaxations, polynomial sums of squares, convergence rate, semidefinite programming, approximation theory Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Category 2: Infinite Dimensional Optimization (Other ) Citation: Download: [PDF] Entry Submitted: 12/12/2016 Modify/Update this entry  
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