Diagonal minus tail forms and Lasserre's sufficient conditions for sums of squares

Abstract

Using our recent results on diagonal minus tail forms, we give an easily tested sufficient condition for a polynomial f(x) = P i2I fixi in IR[x] = IR[x1, . . . , xn], to be a sum of squares of polynomials (sos). We show that the class of polynomials passing this test is wider than the class passing Lasserre’s recent conditions. Another sufficient condition for f to be sos, like Lasserre’s piecewise linear in the fi, is also given.