Positivstellensatz for homogeneous semialgebraic sets (Q895800)
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scientific article; zbMATH DE number 6516544
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positivstellensatz for homogeneous semialgebraic sets |
scientific article; zbMATH DE number 6516544 |
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Positivstellensatz for homogeneous semialgebraic sets (English)
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4 December 2015
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The note contains a complete and elementary proof of a Positivstellensatz for the quadratic module generated by a finite system of homogeneous polynomials. A simple universal denominator and degree bounds are obtained, in the spirit of \textit{B. Reznick} [Math. Z. 220, No. 1, 75--97 (1995; Zbl 0828.12002)]. The result is definitive in its simplicity and will have applications to polynomial optimization.
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positive polynomial
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sum of squares
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universal denominator
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positivestellensatz
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