Symmetrization procedures and convexity in centrally symmetric polytopes

Univariate symmetrization technique has many good properties. In this paper, we adopt the high-dimensional viewpoint, and propose a new symmetrization procedure in arbitrary (convex) polytopes of RdRd with central symmetry. Moreover, the obtained results are used to extend to the arbitrary centrally symmetric polytopes the well-known Hermite–Hadamard inequality for convex functions.