A note on a Lagrangian derivation of a general multi-propotional scaling algorithm

This note describes an efficient minimum information loss solution to the general multi-proportional updating problem. The method provides a robust algorithm which allows additional constraints on groups of elements on the interior of the matrix to be applied, and multi-regional economies to be adjusted simulteneously. A Lagrangian derivation of the scaling algorithm is presented, and the conditions for the existence, uniqueness and convergence of the iterative solutions are explained. The method overcomes restrictions on the bi-proportional method and its extensions.