Preprint series: 03-27 , 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.

Upload: 2003-08-01-08-01