The purpose of this article is to derive and illustrate a method for fitting models involving both convex and log-convex constraints on the probability vector(s) of a (product) multinomial distribution. We give a two-step algorithm to obtain maximum likelihood estimates of the probability vector(s) and show that it is guaranteed to converge to the true solution. Some examples are discussed which illustrate the procedure.
"Maximum likelihood estimates via duality for log-convex models when cell probabilities are subject to convex constraints." Ann. Statist. 26 (5) 1878 - 1893, October 1998. https://doi.org/10.1214/aos/1024691361