Geodesic
Nonnegative polynomials and sums of squares
Blekherman, Grigoriy 1
1 School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160
Journal of the American Mathematical Society, Tome 25 (2012) no. 3, pp. 617-635 Cet article a éte moissonné depuis la source American Mathematical Society

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In the smallest cases where there exist nonnegative polynomials that are not sums of squares we present a complete explanation of this distinction. The fundamental reason that the cone of sums of squares is strictly contained in the cone of nonnegative polynomials is that polynomials of degree $d$ satisfy certain linear relations, known as the Cayley-Bacharach relations, which are not satisfied by polynomials of full degree $2d$. For any nonnegative polynomial that is not a sum of squares we can write down a linear inequality coming from a Cayley-Bacharach relation that certifies this fact. We also characterize strictly positive sums of squares that lie on the boundary of the cone of sums of squares and extreme rays of the cone dual to the cone of sums of squares.
DOI : 10.1090/S0894-0347-2012-00733-4

Blekherman, Grigoriy  1

1 School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, Georgia 30332-0160 
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Blekherman, Grigoriy. Nonnegative polynomials and sums of squares. Journal of the American Mathematical Society, Tome 25 (2012) no. 3, pp. 617-635. doi: 10.1090/S0894-0347-2012-00733-4

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