Robust Optimization is a widespread approach to treat uncertainty in optimization problems. Finding a computationally tractable formulation of the robust counterpart of an uncertain optimization problem is a key step in applying this approach. Techniques for finding a computationally tractable robust counterpart are available for constraints concave in the uncertain parameters. In many problems, however, … Read more
In optimization problems appearing in fields such as economics, finance, or engineering, it is often important that a risk measure of a decision-dependent random variable stays below a prescribed level. At the same time, the underlying probability distribution determining the risk measure’s value is typically known only up to a certain degree and the constraint … Read more
In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It … Read more