  Rado's theorem about permutahedra and dominance order on partitions reveals
that each Schur polynomial is M-convex, or equivalently, it has a saturated
Newton polytope and this polytope is a generalized permutahedron as well. In
this paper we show that the support of each dual $k$-Schur polynomial indexed
by a $k$-bounded partition coincides with that of the Schur polynomial indexed
by the same partition, and hence the two polynomials share the same saturated
Newton polytope. The main result is based on our recursive algorithm to
generate a semistandard $k$-tableau for a given shape and $k$-weight. As
consequences, we obtain the M-convexity of dual $k$-Schur polynomials, affine
Stanley symmetric polynomials and cylindric skew Schur polynomials.
