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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∈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

Original language | English |
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Pages (from-to) | 597-608 |

Journal | Optimization Letters |

Volume | 11 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2017 |

- Polynomial optimization , Taylor’s theorem - grid search

- 10.1007/s11590-016-1023-7
Final published version