Toric geometry of entropic regularization

Entropic regularization is a method for large-scale linear program-ming. Geometrically, one traces intersections of the feasible poly -tope 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.(c) 2023 Elsevier Ltd. All rights reserved.