Remarks on contamination in stochastic programming

If an optimization problem depends on a probability measure, then a complete knowledge of the actual underlying measure is a necessary condition to obtain an exact solution and an exact optimal value. Since this assumption is fulfilled very seldom in real situations, it is mostly necessary to solve such optimization problem with respect to some other (closed) probability measure to obtain at least an approximate optimal solution and an approximate optimal value. The aim of the paper is to investigate a special case of such approximation, in particular, to study the case of a contamination.