Constrained optimization problems under uncertainty with coherent lower previsions

We investigate a constrained optimization problem with uncertainty about constraint parameters. Our aim is to reformulate it as a (constrained) optimization problem without uncertainty. This is done by recasting the original problem as a decision problem under uncertainty. We give results for a number of different types of uncertainty models—linear and vacuous previsions, and possibility distributions—and for two common but different optimality criteria for such decision problems—maximinity and maximality. We compare our approach with other approaches that have appeared in the literature.