  We propose a penalized likelihood method that simultaneously fits the
multinomial logistic regression model and combines subsets of the response
categories. The penalty is non differentiable when pairs of columns in the
optimization variable are equal. This encourages pairwise equality of these
columns in the estimator, which corresponds to response category combination.
We use an alternating direction method of multipliers algorithm to compute the
estimator and we discuss the algorithm's convergence. Prediction and model
selection are also addressed.
