Before revision:   For general buyer valuations or a very large number of buyers, we propose computing market equilibrium using stochastic dual averaging, which finds an approximate equilibrium price vector with high probability.
After revision:  Based on our convex conic reformulation, we develop the first polynomial-time cake-cutting algorithm that achieves Pareto optimality, envy-freeness, and proportionality. For general buyer valuations or a very large number of buyers, we propose computing market equilibrium using stochastic dual averaging, which finds an approximate equilibrium price vector with high probability.