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Federico Piazzon(fpiazzonmath.unipd.it) Abstract: We construct norming meshes for polynomial optimization by the classical Markov inequality on general convex bodies in R^d, and by a tangential Markov inequality via an estimate of Dubiner distance on smooth convex bodies. These allow to compute a (1−eps)approximation to the minimum of any polynomial of degree not exceeding n by O((n/sqrt(eps))^(ad)) samples, with a=2 in the general case, and a=1 in the smooth case. Such constructions are based on three cornerstones of convex geometry, Bieberbach volume inequality and Leichtweiss inequality on the affine breadth eccentricity, and the Rolling Ball Theorem, respectively. Keywords: polynomial optimization, norming mesh, Markov inequality, tangential Markov inequality, Dubiner distance, convex bodies Category 1: Global Optimization (Other ) Citation: Preprint, August 2018 Download: [PDF] Entry Submitted: 08/02/2018 Modify/Update this entry  
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