joint work with Valery Glizer
We consider an finite horizon singular H_{∞} control problem. A regularization of this problem is proposed leading to a new H_{∞} problem with a partial cheap control. The latter is solved by adapting a perturbation technique. Then, it is shown on how accurately the controller, solving this H_{∞} partial cheap control problem, solves the original singular H_{∞} control problem.
joint work with Daniel Kuhn, Wolfram Wiesemann
Leveraging a generalized `primal-worst equals dual-best' duality scheme for robust optimization, we derive from first principles a strong duality result that relates distributionally robust to classical robust optimization problems and that obviates the need to mobilize the machinery of abstract semi-infinite duality theory. In order to illustrate the modeling power of the proposed approach, we present convex reformulations for data-driven distributionally robust optimization problems whose ambiguity sets constitute type-$p$ Wasserstein balls for any $p\in [1,\infty]$.
joint work with Ernst Roos, Jianzhe (Trevor) Zhen, Dick den Hertog, Aharon Ben-Tal
In many problems the uncertain parameters appear in a convex way, which is problematic as no general techniques exist for such problems. In this talk, we provide a systematic way to construct safe approximations to such constraints when the uncertainty set is polyhedral. We reformulate the original problem as a linear adjustable robust optimization problem in which the nonlinearity of the original problem is captured by the new uncertainty set. We demonstrate the quality of the approximations with a study of geometric programming problems and numerical examples from radiotherapy optimization.