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].
| Original language | English |
|---|---|
| Pages (from-to) | 615-625 |
| Number of pages | 11 |
| Journal | Journal of global optimization |
| Volume | 61 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Apr 2015 |
Keywords
- 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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