A bound on the minimum of a real positive polynomial over the standard simplex
Symbolic Computation
2009-02-20 v1
Abstract
We consider the problem of bounding away from 0 the minimum value m taken by a polynomial P of Z[X_1,...,X_k] over the standard simplex, assuming that m>0. Recent algorithmic developments in real algebraic geometry enable us to obtain a positive lower bound on m in terms of the dimension k, the degree d and the bitsize of the coefficients of P. The bound is explicit, and obtained without any extra assumption on P, in contrast with previous results reported in the literature.
Keywords
Cite
@article{arxiv.0902.3304,
title = {A bound on the minimum of a real positive polynomial over the standard simplex},
author = {Saugata Basu and Richard Leroy and Marie-Francoise Roy},
journal= {arXiv preprint arXiv:0902.3304},
year = {2009}
}