2017-03-01
On the convergence rate of grid search for polynomial optimization over the simplex
Publication
Publication
Optimization Letters , Volume 11 - Issue 3 p. 597- 608
We consider the approximate minimization of a given polynomial on the s
tandard 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.
SIAM J. Optim. 25(3) 1498–1514 (2015)] that the relative accuracy of this approximation depends on
r as O(1/r2) if there exists a rational global minimizer. In this note we show that th
e rational minimizer condition is not necessary to obtain the O(1/r2) bound.
| Additional Metadata | |
|---|---|
| Polynomial optimization · Taylor’s theorem - grid search | |
| Nonlinear programming (msc 90C30) | |
| Logistics (theme 3) | |
| Springer | |
| dx.doi.org/10.1007/s11590-016-1023-7 | |
| Optimization Letters | |
| Approximation Algorithms, Quantum Information and Semidefinite Optimization | |
| This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/617.001.351 - Approximation Algorithms, Quantum Information and Semidefinite Optimization | |
| Organisation | Networks and Optimization |
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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, 11(3), 597–608. doi:10.1007/s11590-016-1023-7
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