A bound on the minimum of a real positive polynomial over the standard simplex

Basu, Saugata; Leroy, Richard; Roy, Marie-Francoise

A bound on the minimum of a real positive polynomial over the standard simplex

Authors

Basu, Saugata

Leroy, Richard

Roy, Marie-Francoise

Description

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.