  A variety of approaches has been developed to deal with uncertain
optimization problems. Often, they start with a given set of uncertainties and
then try to minimize the influence of these uncertainties. Depending on the
approach used, the corresponding price of robustness is different. The reverse
view is to first set a budget for the price one is willing to pay and then find
the most robust solution.
  In this article, we aim to unify these inverse approaches to robustness. We
provide a general problem definition and a proof of the existence of its
solution. We study properties of this solution such as closedness, convexity,
and boundedness. We also provide a comparison with existing robustness concepts
such as the stability radius, the resilience radius, and the robust feasibility
radius. We show that the general definition unifies these approaches. We
conclude with examples that demonstrate the flexibility of the introduced
concept.
