Non-Smooth Optimization of the Conditional Value-at-Risk

In this thesis we consider a stochastic optimization problem involving the Conditional Value-at-Risk as a risk measure. This risk measure is equivalently formulated as a non-smooth minimization problem, which is then discretized by using samples from the underlying probability distribution. A primal-dual algorithm is developed to solve the original problem. This algorithm is implemented in MATLAB and a numerical analysis is carried out with two examples motivated by portfolio optimization and power plant operation planning, respectively.