On an extension of Pólya’s Positivstellensatz

Peter James Clair Dickinson, Janez Povh

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)
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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].
Original languageEnglish
Pages (from-to)615-625
Number of pages11
JournalJournal of global optimization
Issue number4
Publication statusPublished - Apr 2015


  • MSC-90C30
  • MSC-11E25
  • MSC-14P05
  • MSC-14P10
  • Non-negativity certificate
  • IR-95419
  • Polynomial optimization
  • Positivstellensatz
  • EWI-25767
  • METIS-312506
  • Semialgebraic set
  • n/a OA procedure


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