  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 natural
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 naturally adjusts
demand within a consumption cycle.
