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

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)597-608
JournalOptimization Letters
Issue number3
StatePublished - Mar 2017

    Research areas

  • Polynomial optimization , Taylor’s theorem - grid search
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