Abstract: Sous les facettes des Polyèdres, sous les facettes, les polyèdres

In this survey we describe some results on combinatorial polyhedra and their applications in optimization. We begin by recalling the Simplex method, then we give some elementary properties of polyhedra, particularly the Weyl theorem. We thus introduce the combinatorial polyhedra, we give the characterization of the convex hull of the independant subsets common to two matroids on the same set. We thus give the description of the classical approximation of the travelling salesman polyhedron. We thus describe some interior point methods, and deduce, in one important practical case, the polynomial equivalence between separation and optimization on polyhedra. We end this survey noting some other points of view on combinatorial optimization.