Optimization Under Uncertainty
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Robust optimization is a very active field of research. In this chapter, we show that translation invariant functionals can be considered in order to describe many concepts of robustness and stochastic optimization which are well known from scalar optimization under uncertainty as special cases of a scalarization by means of translation invariant functionals. Based on this unified approach to robustness and stochastic optimization, it is possible to derive new concepts of robustness in scalar optimization under uncertainty. Moreover, we explain that the well-studied properties of translation invariant functionals allow the establishment of useful relationships to multiobjective optimization problems.