Let $C\subset N_{\mathbb{R}}$ be a convex polyhedron. A function $f\colon C\to\mathbb{R}$ is piecewise affine if there a finite cover of $C$ by closed subsets such that the restriction of $f$ to each of these subsets is an affine function. A concave function $f\colon N_{\mathbb{R}}\to{\underline{\mathbb{R}}}$ is said to be piecewise affine if ${\operatorname{dom}}(f)$ is a convex polyhedron and the restriction $f|_{{\operatorname{dom}}(f)}$ piecewise affine.