  In this article, we propose a geometric programming method in order to
compute lower bounds for real polynomials. We provide new sufficient conditions
for polynomials to be nonnegative as well as to have a sum of binomial squares
representation. These criteria rely on the coefficients and the support of a
polynomial and generalize all previous ones by Lasserre, Ghasemi, Marshall,
Fidalgo and Kovacec to polynomials with arbitrary simplex Newton polytopes.
  This generalization yields a geometric programming approach for computing
lower bounds for polynomials that significantly extends the geometric
programming method proposed by Ghasemi and Marshall. Furthermore, it shows that
geometric programming is strongly related to nonnegativity certificates based
on sums of nonnegative circuit polynomials, which were recently introduced by
the authors.
