A PTAS for the minimization of polynomials of fixed degree over the simplex - Extended abstract

One may assume w.l.o.g. that p(x) is a homogeneous polynomial (form). Indeed, as observed in [2], if p(x) = ∑d l=0 pl(x), where pl(x) is homogeneous of degree l, then minimizing p(x) over ∆ is equivalent to minimizing the degree d form p(x) := ∑d l=0 pl(x)( ∑n i=1 xi) . Problem (1) is an NP-hard problem, already for forms of degree d = 2, as it contains the maximum stable set problem. Indeed, for a graph G with adjacency matrix A, the maximum size α(G) of a stable set in G can be expressed as 1 α(G) = min x∈∆ x (I +A)x