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Published in:
2012 | OriginalPaper | Chapter
Chapter 1 Representation of Positive Polynomials
Authors : Roberto Cominetti, Francisco Facchinei, Jean B. Lasserre
Published in: Modern Optimization Modelling Techniques
Publisher: Springer Basel
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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
).