The goal of this work is to provide a simple condition on a multivariate polynomial p such that the convex dual function defined in a previous work [5] is coercive (infinite at infinity). It is based on the fact that data points obtained from tensorization of the roots of the third and fourth kind Chebyshev polynomials possess a strong stability property, so they are (nearly) optimal. The stability property is fundamentally connecte to the Lebesgue stability constant of Chebyshev interpolation. It has the consequence that G has a global minimum, which justifies on the hypercube the gradient descent algorithms proposed in [5]. A corollary is a constructive representation of p as a sum of squares (SOS) endowed with the Schmüdgen's Positivstellensatz structure.