  Entropic regularization is a method for large-scale linear programming.
Geometrically, one traces intersections of the feasible polytope with scaled
toric varieties, starting at the Birch point. We compare this to log-barrier
methods, with reciprocal linear spaces, starting at the analytic center. We
revisit entropic regularization for unbalanced optimal transport, and we
develop the use of optimal conic couplings. We compute the degree of the
associated toric variety, and we explore algorithms like iterative scaling.
