An efficient sum of squares nonnegativity certificate for quaternary quartic

Working paper

We give an embarrassingly simple construction of a representation of a nonnegative 4-ary homogeneous polynomial $f$ (i.e. a form) of degree 4 as a ratio $p/q$ of a sum of squares forms of degrees 8 and 4, respectively. This allows an efficient check of nonnegativity of $f$ using semidefinite optimization. No similar results were known for forms of degree greater than 2 in more than 3 variables.

Authors: Pasechnik, D

• Publication status: Not published
• Peer review status: Not peer reviewed
• Publication date: 2015-11-11
• Keywords: math.AG; math.OC; math.CA