Let Z be a compact set of the real space ℜ with at least n + 2 points; f, h1, h2 : Z → ℜ continuous function, h1, h2 strictly positive and P(x,z), x := (x0,..., xn)τ ∈ ℜn+1, z ∈ ℜ, a polynomial of degree at most n. Consider a feasible set M := {x ∈ ℜn+1 | ∀z ∈ Z, –h2(z) ≤ P(x,z) – f(z) ≤ h1(z)}. Here it is proved the null vector 0 of ℜn+1 belongs to the compact convex hull of the gradients ± (1,z,..., zn), where z ∈ Z are the index points in which the constraint functions are active for a given x* ∈ M, if and only if M is a singleton.
