  We introduce a new technique, which we call the boundary method, for solving
semi-discrete optimal transport problems with a wide range of cost functions.
The boundary method reduces the effective dimension of the problem, thus
improving complexity. For cost functions equal to a p-norm with p in
(1,infinity), we provide mathematical justification, convergence analysis, and
algorithmic development. Our testing supports the boundary method with these
p-norms, as well as other, more general cost functions.
