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 corresponding surplus functions. In particular, we explicitly convexity parameter choice associated with generalized extreme value models, and specifically nested logit models. Incorporated into subgradient schemes, lead to a probabilistic interpretations iteration steps. As illustration, discuss an economic application in consumer theory. The dual averaging scheme programming adjusts demand within consumption cycle.