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

2014/02/25 by Sadik Iliman, Iliman, Sadik, Timo de Wolff +1 · 2 citations
Computer Science · Engineering · #12D15 #14P99 #52B20 #90C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Formal Methods in Verification #Optimization and Control (math.OC) #Polynomial and algebraic computation #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1402.6185

openalex publication_date 2014/02/25 · openalex created_date 2022/09/25 · openalex updated_date 2026/07/28

Abstract

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

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• Lower Bound for a Polynomial on a product of hyperellipsoids using geometric programming
• Non-negative polynomials without hyperbolic certificates of non-negativity

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