- On the convergence rate of grid search for polynomial optimization over the simplex Etienne de Klerk(E.deKlerkuvt.nl) Monique Laurent(M.Laurentcwi.nl) Zhao Sun(Zhao.Sunpolymtl.ca) Juan Vera(j.c.veralizcanouvt.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) 1498--1514 (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: 10/05/2015Entry Accepted: 10/05/2015Entry Last Modified: 10/05/2015Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.