Scenario decomposable subgradient projection method for two-stage stochastic programming with convex risk measures

We consider the general two-stage convex stochastic programs with discrete distribution, in which the risk measure is only assumed to be convex and monotonic, not necessarily to be coherent or have special structures. We propose a scenario decomposition framework which incorporates subgradient computation and the incremental constraint projection steps. The decomposition of the algorithm is based on the scenario-wise separability of these computations. We analyze the convergence and local rate of convergence of the proposed method under mild conditions. This method is further applied to a class of distributionally robust two-stage stochastic programs. Numerical results of a practical multi-product assembly model are reported to demonstrate the effectiveness of the proposed method.