Primal-dual hybrid gradient method for distributionally robust optimization problems

We focus on the discretization approach to distributionally robust optimization (DRO) problems and propose a numerical scheme originated from the primal-dual hybrid gradient (PDHG) method that recently has been well studied in convex optimization area. Specifically, we consider the cases where the ambiguity set of the discretized DRO model is defined through the moment condition and Wasserstein metric, respectively. Moreover, we apply the PDHG to a portfolio selection problem modelled by DRO and verify its efficiency.