On the convergence rate of grid search for polynomial optimization over the simplex

@article{Klerk2017OnTC,
  title={On the convergence rate of grid search for polynomial optimization over the simplex},
  author={Etienne de Klerk and Monique Laurent and Zhao Sun and Juan C. Vera},
  journal={Optimization Letters},
  year={2017},
  volume={11},
  pages={597-608}
}
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 $${r} \in \mathbb {N}$$r∈N. It was shown in De Klerk et al. (SIAM J Optim 25(3):1498–1514, 2015) that the accuracy of this approximation depends on r as $$O(1/r^2)$$O(1/r2) if there exists a rational global minimizer. In this note we show that the rational minimizer condition is not necessary to obtain the $$O(1/r^2)$$O… 
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