Given a contingency table of nonnegative reals in which the internal entries do not sum to the corresponding marginals, there is often the need to adjust internal entries to achieve additivity. In many applications, the objective is to have zero entries in the original table remain zero in the table and positive entries remain positive. Not all two-way contingency tables can be adjusted to achieve additivity subject to these constraints, and in (Fagan and Greenberg, 1987) the authors presented a procedure to determine whether a table can be adjusted, and such adjustable tables were called feasible.

In general, given a feasible table one seeks a derived table that is close. For every criterion of closeness a different objective function must be optimized. Three of the most cited criteria of closeness are: (a) Raking, (b) Maximum Likelihood, and (c) Minimum Chi-Square. In this paper we provide algorithms which converge to a revised table optimizing each objective function. We provide a unified method showing that each of the algorithms converges to a unique table of specified closeness.