Abstract: The aim of this project is to perform first steps into discrete symplectic geometry by developing and implementing algorithms to compute the Ekeland-Hofer capacity of convex polytopes in a symplectic vector space. These algorithms are based on the dual action principle of Clarke. There are several interesting symplectic and optimization questions connected to this. We expect these algorithms to give us insights into challenging open questions in symplectic topology, billiard dynamics and convex geometry.