On the convergence rate of grid search for polynomial optimization over the simplex
de Klerk,Etienne Laurent,Monique Sun,Zhao Vera,J.C.
de Klerk,Etienne
Laurent,Monique
Sun,Zhao
Vera,J.C.
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∈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
Description
Date
2017-03
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Volume Title
Publisher
Research Projects
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Keywords
Polynomial optimization, Taylor’s theorem - grid search
Citation
de Klerk, E, Laurent, M, Sun, Z & Vera, J C 2017, 'On the convergence rate of grid search for polynomial optimization over the simplex', Optimization Letters, vol. 11, no. 3, pp. 597-608. https://doi.org/10.1007/s11590-016-1023-7