The theorem Optimization/Séparation is a consequence the Méthode of the ellipsoid. It constitutes a result (very difficult to show) major in combinative Optimization which establishes the link between the Approche polyèdrale and the Algorithmique. This result establishes equivalence, from the point of view of the algorithmic complexity, between " optimizer" and " séparer" on the same polyhedron. A polyhedron $P$ of $\backslash \; mathbb\; R^n$ is consisted the whole of the points $X\; \backslash \; in\; \backslash \; mathbb\; R^n$ satisfying a number arbitrarily large but finished linear inequalities (i.e of the form $\backslash \; sum\_\; \{i=1\}\; ^\; \{i=n\}\; a\_ix\_i\; \backslash \; B$).

* Optimizer on $P$ consists in determining $\backslash \; max\_\; \{X\; \backslash \; in\; P\}\; F\; (X)$ for any linear function $F\; (X)$.

* Séparer on $P$ consists in determining if $\backslash \; bar\; X\; \backslash \; in\; P$ or not, for any point $\backslash \; bar\; X\; \backslash \; in\; \backslash \; mathbb\; R^n$, and so not to determine a hyperplane separating $\backslash \; bar\; X$ from $P$ (i.e to find an inequality linear violated by $\backslash \; bar\; X$ but satisfied by any point with $P$).

Théorème Optimization/Séparation (Mr. Grötschel, L. Lovász, A. Shrijver, 1981) One can optimize on a polyhedron in polynomial time if and only if one can separate on this polyhedron in polynomial time .