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In this article, we propose a geometric programming method in order tocompute lower bounds for real polynomials. We provide new sufficient conditionsfor polynomials to be nonnegative as well as to have a sum of binomial squaresrepresentation. These criteria rely on the coefficients and the support of apolynomial 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 computinglower bounds for polynomials that significantly extends the geometricprogramming method proposed by Ghasemi and Marshall. Furthermore, it shows thatgeometric programming is strongly related to nonnegativity certificates basedon sums of nonnegative circuit polynomials, which were recently introduced bythe authors.

Lower Bounds for Polynomials with Simplex Newton Polytopes Based on Geometric Programming