Let g λ (Z) = g 1 (Z) + g 2 (Z) + g 3 (Z) + g 4 (Z) where For g 2 (Z), since coefficients of all terms are nonnegative, we can use the fact to reduce g 2 (Z) into an equivalent quadratic form (Freedman and Drineas, 2005).
max Z g 2 (Z) is equivalent to  which is graph representable because coefficients of all the quadratic terms are non-negative.