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Etienne de Klerk(E.deKlerkuvt.nl) Abstract: We consider the approximate minimization of a given polynomial on the standard simplex, obtained by taking the minimum value over all rational grid points with given denominator ${r} \in \mathbb{N}$. It was shown in [De Klerk, E., Laurent, M., Sun, Z.: An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution. {\em SIAM J. Optim.} 25(3) 14981514 (2015)] that the relative accuracy of this approximation depends on $r$ as $O(1/r^2)$ if there exists a rational global minimizer. In this note we show that the rational minimizer condition is not necessary to obtain the $O(1/r^2)$ bound. Keywords: Polynomial optimization, Taylor's theorem Category 1: Global Optimization (Theory ) Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Technical report, Tilburg University, CWI Amsterdam, and Polytechnique Montreal, October 2015. Download: [PDF] Entry Submitted: 10/05/2015 Modify/Update this entry  
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