@unpublished{AdelhuetteBiefelKuchlbaueretal., author = {Adelh{\"u}tte, Dennis and Biefel, Christitan and Kuchlbauer, Martina and Rolfes, Jan}, title = {Pareto Robust optimization on Euclidean vector spaces}, abstract = {Pareto efficiency for robust linear programs was introduced by Iancu and Trichakis in [9]. We generalize their approach and theoretical results to robust optimization problems in Euclidean spaces with linear uncertainty. Additionally, we demonstrate the value of this approach in an exemplary manner in the area of robust semidefinite programming (SDP). In particular, we prove that computing a Pareto robustly optimal solution for a robust SDP is tractable and illustrate the benefit of such solutions at the example of the maximal eigenvalue problem. Furthermore, we modify the famous algorithm of Goemans and Williamson [8] in order to compute cuts for the robust max cut problem that yield an improved approximation guarantee in non-worst-case scenarios.}, language = {en} } @article{AdelhuetteAssmannGonzalezGrandonetal.2017, author = {Adelh{\"u}tte, Dennis and Aßmann, Denis and Gonz{\`a}lez Grand{\`o}n, Tatiana and Gugat, Martin and Heitsch, Holger and Liers, Frauke and Henrion, Ren{\´e} and Nitsche, Sabrina and Schultz, R{\"u}diger and Stingl, Michael and Wintergerst, David}, title = {Joint model of probabilistic/robust (probust) constraints applied to gas network optimization}, doi = {10.1007/s10013-020-00434-y}, year = {2017}, abstract = {Optimization tasks under uncertain conditions abound in many real-life applications. Whereas solution approaches for probabilistic constraints are often developed in case the uncertainties can be assumed to follow a certain probability distribution, robust approaches are usually used in case solutions are sought that are feasible for all realizations of uncertainties within some pre-defined uncertainty set. As many applications contain different types of uncertainties that require robust as well as probabilistic treatments, we deal with a class of joint probabilistic/robust constraints as its appears in optimization problems under uncertainty. Focusing on complex uncertain gas network optimization problems, we show the relevance of this class of problems for the task of maximizing free booked capacities in an algebraic model for a stationary gas network. We furthermore present approaches for their solution. Finally, we study the problem of controlling a transient system that is governed by the wave equation. The task consists in determining controls such that a certain robustness measure remains below some given upper bound, with high probability.}, language = {en} }