This report is part of ISTC's Technical Report Series. Mention of trade names or commercial products does not constitute endorsement or recommendation for use. iii Acknowledgments We thank our colleagues from the Illinois Sustainable Technology Center (ISTC),

This paper presents a general, self-contained treatment of convexity or intersection cuts. It describes two equivalent ways of generating a cut — via a convex set or a concave function — and a notion of strong cuts. We then characterize the structure of the sets and functions that generate strong cuts. We then specialize the framework to the case of mixed-integer linear programming (MIP). For t...