On an extension of Pólya’s Positivstellensatz

In this paper we provide a generalization of a Positivstellensatz by Pólya [Pólya in Naturforsch Ges Zürich 73:141–145 1928 ]. We show that if a homogeneous polynomial is positive over the intersection of the non-negative orthant and a given basic semialgebraic cone (excluding the origin), then ther...

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Bibliographic Details
Published in:Journal of global optimization 2015-04, Vol.61 (4), p.615-625
Main Authors: Dickinson, Peter J. C., Povh, Janez
Format: Article
Language:English
Subjects:
Algebra
Approximation
Computer Science
Intersections
Linear programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Optimization algorithms
Origins
Polynomials
Proving
Real Functions
Studies
Theorems
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Summary:In this paper we provide a generalization of a Positivstellensatz by Pólya [Pólya in Naturforsch Ges Zürich 73:141–145 1928 ]. We show that if a homogeneous polynomial is positive over the intersection of the non-negative orthant and a given basic semialgebraic cone (excluding the origin), then there exists a “Pólya type” certificate for non-negativity. The proof of this result uses the original Positivstellensatz by Pólya, and a Positivstellensatz by Putinar and Vasilescu [Putinar and Vasilescu C R Acad Sci Ser I Math 328(7) 1999 ].
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-014-0196-9