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 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.
|Place of Publication||Ithaca|
|Publisher||Cornell University Library|
|Number of pages||17|
|Publication status||Published - 9 Jul 2014|
|Name||Preprint at arXiv|