  We give approximation algorithms for the edge expansion and sparsest cut with
product demands problems on directed hypergraphs, which subsume previous graph
models such as undirected hypergraphs and directed normal graphs.
  Using an SDP formulation adapted to directed hypergraphs, we apply the SDP
primal-dual framework by Arora and Kale (JACM 2016) to design polynomial-time
algorithms whose approximation ratios match those of algorithms previously
designed for more restricted graph models. Moreover, we have deconstructed
their framework and simplified the notation to give a much cleaner presentation
of the algorithms.
