On the minimum of a positive polynomial over the standard simplex

摘要

We present a new positive lower bound for the minimum value taken by a polynomial P with integer coefficients in k variables over the standard simplex of R~k, assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize r of the coefficients of P and improves all the previous bounds for arbitrary polynomials which are positive over the simplex.