2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164398We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic subset K of Rn. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define K.Algebraic GeometryOptimization and Control14P10; 90C22text