Separating inequalities for nonnegative polynomials that are not sums of squares

Details Separating inequalities for nonnegative polynomials that are not sums of squares Separating inequalities for nonnegative polynomials that are not sums of squares

2012-01-19

arxiv.org/abs/1201.4061v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

Ternary sextics and quaternary quartics are the smallest cases where there exist nonnegative polynomials that are not sums of squares (SOS). A complete classification of the difference between these cones was given by G. Blekherman via analyzing the corresponding dual cones. An exact computation of the extreme rays in order to separate a fixed nonnegative polynomial that is not SOS is difficult. We provide a method substantially simplifying this computation for certain classes of polynomials on the boundary of these cones. In particular, our method yields separating extreme rays for almost every nonnegative ternary sextic with at least seven zeros. As an application to further instances, we compute a rational certificate proving that the Motzkin polynomial is not SOS.

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