Ill-posedness in continuous linear optimization via partitions of the space of parameters

In this paper we consider the parameter space of continuous linear optimization problems with a given decision space and a given index set. We consider different partitions of this space, on the basis of the primal, the dual, and the primal-dual status of each parameter. We define ill-posedness and relative ill-posedness w.r.t. a given set and absolute ill-posedness w.r.t. a given family of sets. These concepts are characterized for the elements of the partitions considered in this paper