Optimization and Positivity Certificates of Rational Functions using Bernstein Form. arXiv:1906.11037
Preprint, arXiv:1906.11037 [math.OC] (2019).
Summary: Rational functions of total degree \(l\) in n variables have a representation in the Bernstein form defined over \(n\) dimensional simplex. The range of a rational function is bounded by the smallest and the largest rational Bernstein coefficients over a simplex. Convergence properties of the bounds to the range are reviewed. Algebraic identities certifying the positivity of a given rational function over a simplex are given. Subsequently, a bound established in this work does not depend on the given dimension.
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