On an extension of Pólya’s Positivstellensatz

Peter Dickinson () and Janez Povh ()

Journal of Global Optimization, 2015, vol. 61, issue 4, 615-625

Abstract: 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 ]. Copyright Springer Science+Business Media New York 2015

Keywords: Positivstellensatz; Semialgebraic set; Non-negativity certificate; Polynomial optimization; 11E25; 14P05; 14P10; 90C30 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-014-0196-9

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