An Error Analysis for Polynomial Optimization over the Simplex Based on the Multivariate Hypergeometric Distribution

  title={An Error Analysis for Polynomial Optimization over the Simplex Based on the Multivariate Hypergeometric Distribution},
  author={Etienne de Klerk and Monique Laurent and Zhao Sun},
  journal={SIAM J. Optim.},
We study the minimization of fixed-degree polynomials over the simplex. This problem is well-known to be NP-hard, as it contains the maximum stable set problem in graph theory as a special case. In this paper, we consider a rational approximation by taking the minimum over the regular grid, which consists of rational points with denominator $r$ (for given $r$). We show that the associated convergence rate is $O(1/r^2)$ for quadratic polynomials. For general polynomials, if there exists a… Expand
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