Consider the integer linear optimization or integer linear programming problem

$\mathrm{max}\{{c}^{T}x|Ax\le b,x\in {\mathbb{Z}}^{n}\},A\in {\mathbb{Z}}^{m\times n},b\in {\mathbb{Z}}^{m}.$

(3.12)

An important consequence of Theorem (3.3) is that for a rational polyhedron
$P=\{x\in {\mathbb{F}}^{n}|Ax\le b\}$
, the convex hull of the set of integer points S = P ∩
^{n}
in P is again a rational polyhedron. Therefore, in principle, the integer linear optimization ...

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