Basic Distributionally Robust Optimization

This chapter provides an overview of the general theory of distributionally robust optimization (DRO). It begins with the basic ideas of this technique, followed by an explanation of distributionally robust uncertainties, including worst-case expectations, robust chance constraints, and distributionally robust risk measures. Subsequently, a model of two-stage DRO is presented, which will serve as the main optimization framework applied to various energy storage sizing problems in the application part of this book. Finally, some general reformulation methods between different types of distributionally robust uncertainties are explained. These methods are applicable to any type of ambiguity set.