Narrow Results

This paper is about the analysis of sets of constraints, with no further assumptions. We explore the relationship between the minimal representation problem and a certain set covering problem of Boneh. This provides a framework that shows the connection between minimal representations, irreducible infeasible systems, minimal infeasibility sets, as well as other attributes of the preprocessing of mathematical programs. The framework facilitates the development of preprocessing algorithms for a variety of mathematical programs. As some such algorithms require random sampling, we present results to identify those sets of constraints for which all information can be sampled with nonzero probability.