  The discrete optimal transport (OT) problem, which offers an effective
computational tool for comparing two discrete probability distributions, has
recently attracted much attention and played essential roles in many modern
applications. This paper proposes to solve the discrete OT problem by applying
a squared smoothing Newton method via the Huber smoothing function for solving
the corresponding KKT system directly. The proposed algorithm admits appealing
convergence properties and is able to take advantage of the solution sparsity
to greatly reduce computational costs. Moreover, the algorithm can be extended
to solve problems with similar structures including the Wasserstein barycenter
(WB) problem with fixed supports. To verify the practical performance of the
proposed method, we conduct extensive numerical experiments to solve a large
set of discrete OT and WB benchmark problems. Our numerical results show that
the proposed method is efficient compared to state-of-the-art linear
programming (LP) solvers. Moreover, the proposed method consumes less memory
than existing LP solvers, which demonstrates the potential usage of our
algorithm for solving large-scale OT and WB problems.
