Recent Advances in Robust Optimization

We will briefly survey the state of the art of the Robust Optimization (RO) methodology for solving convex conic optimization problems, both static and dynamic (multi-stage) emphasizing issues of computational tractability, and probabilistic guarantees satisfied by the optimal robust solution. We then introduce a recent extension of the methodology in which the solution is required to exhibit a controlled deterioration in the performance for uncertain data outside the nominal uncertainty set. Finally we discuss uncertainly affected linear control systems and introduce a novel reparameterization scheme that converts the, otherwise nonconvex, control problem into a convex programming one.