We investigate a generic, informal constrained optimization problem for which there is uncertainty about a constraint parameter. To be able to deal with it formally, we reformulate it as a decision problem under uncertainty, in which the uncertainty is in general expressed using a set of probabilities. Our goal is to end up with a constrained optimization problem without uncertainty and this for different classes of sets of probabilities and different optimality criteria. Some results will be presented, and the problem and our approach will be illustrated using a pair of simple engineering problems.