### 2003-27

by Bosse, Hartwig, Grötschel, Martin, Henk, Martin.

**Series:** 2003-27, Preprints

- MSC:
- 52B11 $n$-dimensional polytopes
- 14P10 Semialgebraic sets and related spaces
- 90C27 Combinatorial optimization

**Abstract:**

Our main result is that every n-dimensional polytope can be described by at most (2n-1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n-2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.

**Keywords:**