Work

Optimization and Positivity Certificates of Rational Functions using Bernstein Form

Year: 2019

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1906.11037

Authors: Hamadneh, Tareq, Al-Zoubi, Hassan, Alzaareer, Hamza, Wisniewski, Rafael

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2956011008

Cites: 24

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Related to: 10