The seminar consists of two parts, where the first part is an introduction to hierarchical programs and discretization methods for their solution. We discuss important members of the family of hierarchical programs such as (generalized) semi-infinite and bilevel programs.In particular, we highlight the connections between different kinds hierarchical programs and reformulations from one kind to another. Furthermore, we give a brief introduction into a family of discretization algorithms for hierarchical programs that is built on the algorithm proposed in (Blankenship and Falk in Journal of Optimization Theory and Applications 19(2):261-281, 1976).In the second part, we consider the problem of categorizing contingencies in power grids under uncertainty in order to support the provision of (n-1)-reliability. Following previous work (Fliscounakis et al. in IEEE Transactions on Power Systems 28(4):4909-4917, 2013), our aim is to categorize contingencies according to the preventive control actions that are required to guarantee nominal operation of a power grid under uncertainty and optimal corrective control actions.This problem formulation results in an existence-constrained semi-infinite program (ESIP), which belongs to the family of hierarchical programs. As a power grid model, we employ the DC power flow approximation together with disjunctive models for load distribution, bus merging and splitting, and phase shifting transformers (Djelassi et al. in Power Systems Computation Conference, 2018).Due to the lack of rigorous algorithms for the solution of ESIPs, prior considerations of the categorization problem were limited to solving a feasibility problem. Now, our recently proposed algorithm for the global solution of ESIPs absent convexity assumptions (Djelassi and Mitsos in Journal of Optimization Theory and Applications, submitted 2019) enables the solution of the categorization problem. We present the results of a screening of contingencies on a large-scale power grid instance, where we solve the categorization problem for each member of a set of contingencies. We discuss the information that can be gained from categorization of contingencies as well as the tractability of the proposed approach for large-scale contingency screenings.