Maximum likelihood estimation via duality for cell probabilities subject to convex and log-convex constraints

This article proposes a method for fitting models subject to a convex and log-convex constraint on the probability vector of a product multinomial (binomial) distribution. We present an iterative algorithm for finding the restricted maximum likelihood estimates (MLEs) of the probability vector and show that the algorithm converges to the true solution. Some examples are discussed to illustrate the method.