On the minimum of a positive polynomial over the standard simplex

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 Rk , assuming that P is positive on the simplex. This bound depends only on the number of variables k, the degree d and the bitsize τ of the coefficients of P and improves all previous bounds for arbitrary polynomials which are positive over the simplex.

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Gabriela Jeronimo, Daniel Perrucci
• Keywords: JSC 2010, Polynomials, Simplex, Standard Simplex