On the minimum of a positive polynomial over the standard simplex
Algebraic Geometry
2009-06-25 v1 Symbolic Computation
Abstract
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, the degree and the bitsize of the coefficients of P and improves all previous bounds for arbitrary polynomials which are positive over the simplex.
Cite
@article{arxiv.0906.4377,
title = {On the minimum of a positive polynomial over the standard simplex},
author = {Gabriela Jeronimo and Daniel Perrucci},
journal= {arXiv preprint arXiv:0906.4377},
year = {2009}
}