A solution method for nonlinear convex stochastic optimization problems

The paper considers nonlinear convex stochastic two-stage optimization problems with stochasticity in the objective as well as in the right-hand side. The support of the underlying distribution function is assumed to be contained in polytopes (for computational reasons we concentrate on specially shaped polytopes like rectangles and simplices). Applying duality theory we may construct for the second-stage objective easily integrable lower and upper approximating functions that are linear in the random variables or at least separately linear in their components. By construction the approximating functions support the second-stage objective at certain points chosen with respect to the distribution function and independent of the second-stage objective, therefore preserving convexity of the overall objective in the first-stage decision.