An MM Algorithm for Estimating the MNL Model with Product Features

The multinomial logit (MNL) model is a workhorse model for modeling customer demand in many fields including operations, econometrics and marketing. In this work, we present a fast algorithm for solving the likelihood maximization problem for the MNL model with product features. Our algorithm falls under the general framework of minorize-maximize (MM) procedures and we show that it results in an efficient iterative procedure with closed-form updates. We establish a necessary and sufficient condition under which the optimization problem has a unique and bounded solution and establish convergence of our proposed algorithm to the global optimal solution.