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. (c) 2012 Elsevier B.V. All rights reserved.