## Lattice closures of polyhedra

Given $P\subset\R^n$, a mixed-integer set $P^I=P\cap (\Z^{t}\times\R^{n-t}$), and a $k$-tuple of $n$-dimensional integral vectors $(\pi_1, \ldots, \pi_k)$ where the last $n-t$ entries of each vector is zero, we consider the relaxation of $P^I$ obtained by taking the convex hull of points $x$ in $P$ for which $ \pi_1^Tx,\ldots,\pi^T_kx$ are integral. We then define the $k$-dimensional … Read more