Discrete Choice Prox-Functions on the Simplex

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps. As illustration, we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming adjusts demand within a consumption cycle.