The paper presents a matrix scaling problem called truncated scaling and describes applications arising in economics, urban planning, and statistics. It associates a dual pair of convex optimization problems to the scaling problem and proves that the existence of a solution for the truncated scaling problem is characterized by the attainment of the infimum in the dual optimization problem. The paper shows that optimization problems used by Bacharach, Bachem and Korte, Eaves et al., Marshall and Olkin and Rothblum and Schneider to study scaling problems can be derived as special cases of the dual problem for truncated scaling. It presents computational results for solving truncated scaling problems using dual coordinate descent, thereby showing that truncated scaling provides a framework for modeling and solving large-scale matrix scaling problems.
