Maximum likelihood estimates via duality for log-convex models when cell probabilities are subject to convex constraints

The purpose of this article is to derive and illustrate a method for fittin g models involving both convex and log-convex constraints on the probabilit y vector(s) of a (product) multinomial distribution. We give a two-step alg orithm to obtain maximum likelihood estimates of the probability vector(s) and show that it is guaranteed to converge to the true solution. Some examp les are discussed which illustrate the procedure.