Symmetric semialgebraic sets and nonnegativity of symmetric polynomials
Abstract
The question of how to certify the nonnegativity of a polynomial function lies at the heart of Real Algebra and it also has important applications to Optimization. In the setting of symmetric polynomials Timofte provided a useful way of certifying nonnegativity of symmetric polynomials that are of a fixed degree. In this note we present more general results which naturally generalize Timofte's setting. We investigate families of polynomials that allow special representations in terms of powersum polynomials.These in particular also include the case of symmetric polynomials of fixed degree. Therefore, we recover the consequences of Timofte's original statements as a corollary. Thus, this note also provides an alternative and simple proof of Timofte's original statements.
 Publication:

arXiv eprints
 Pub Date:
 September 2014
 arXiv:
 arXiv:1409.0699
 Bibcode:
 2014arXiv1409.0699R
 Keywords:

 Mathematics  Optimization and Control
 EPrint:
 6 pages