Abstract
In one dimension, the ring \({\mathbb{R}} [x]\) of real polynomials in a single variable has the fundamental property (Theorem 1.6) that every nonnegative polynomial \(p \in \mathbb{R} [x]\) is a sum of squares of polynomials, that is, \(p(x) \geq 0, \forall_{x} \in \mathbb{R}\,\,\,\Longleftrightarrow\,\,\,p(x) = \sum\limits_{i=1}^{k} h_i(x)^{2}, \forall_{x} \in \mathbb{R}\), for finitely many polynomials (h i).
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© 2012 Springer Basel
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Cominetti, R., Facchinei, F., Lasserre, J.B. (2012). Chapter 1 Representation of Positive Polynomials. In: Modern Optimization Modelling Techniques. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0291-8_1
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DOI: https://doi.org/10.1007/978-3-0348-0291-8_1
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0290-1
Online ISBN: 978-3-0348-0291-8
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