Describing Polyhedra by Polynomial Inequalities


A new method of describing polyhedra is implied by results in real-algebraic geometry.

The aim of this project is to further the new proof technique and implement the algorithm that is the basis of this result. New strategies for the solution of combinatorial optimization problems will be examined by adapting the results to special classes of combinatorially interesting polyhedra. Finally, general principles used in the theory of polyhedra, such as homgenization, are to be investigated with respect to their aplicability in algebraic geometry.