An error analysis for polynomial optimization over the simplex based on the multivariate hypergeometric distribution
Abstract
We study the minimization of fixeddegree polynomials over the simplex. This problem is wellknown to be NPhard, 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 rational global minimizer over the simplex, we show that the convergence rate is also of the order $O(1/r^2)$. Our results answer a question posed by De Klerk et al. (2013) and improves on previously known $O(1/r)$ bounds in the quadratic case.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.2108
 Bibcode:
 2014arXiv1407.2108D
 Keywords:

 Mathematics  Optimization and Control;
 90C26;
 90C30
 EPrint:
 17 pages