Optimization and Positivity Certificates of Rational Functions using Bernstein Form
Optimization and Control
2019-06-27 v1
Abstract
Rational functions of total degree in n variables have a representation in the Bernstein form defined over 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.
Cite
@article{arxiv.1906.11037,
title = {Optimization and Positivity Certificates of Rational Functions using Bernstein Form},
author = {Tareq Hamadneh and Hassan Al-Zoubi and Hamza Alzaareer and Rafael Wisniewski},
journal= {arXiv preprint arXiv:1906.11037},
year = {2019}
}