Positivstellensatz for homogeneous semialgebraic sets
type: Item
instance of: scholarly article
title: Positivstellensatz for homogeneous semialgebraic sets
zbMATH Open document ID: 1358.14038
author: Aleksandra Gala-Jaskórzyńska
author: Krzysztof Kurdyka
author: Katarzyna Kuta
author: Stanisław Spodzieja
published in: Archiv der Mathematik
publication date: 2015-12-04T00:00:00Z
review text: 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.
reviewed by: Mihai Putinar
Mathematics Subject Classification ID: 14P10
Mathematics Subject Classification ID: 12D15
Mathematics Subject Classification ID: 26B25
zbMATH DE Number: 6516544
zbMATH Keywords: positive polynomial
zbMATH Keywords: sum of squares
zbMATH Keywords: universal denominator
zbMATH Keywords: positivestellensatz
MaRDI profile type: Publication
full work available at URL: s00013-015-0822-x
OpenAlex ID: W2116921991
Wikidata QID: Q59403458
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DOI: 10.1007/S00013-015-0822-X
description: scientific article; zbMATH DE number 6516544