R U T C O R

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 strongest cuts. We characterize the structure of the sets and functions that generate strongest cuts. We then specialize the framework to the case of 0-1 mixed-integer linear programming (MIP). For this case, we formulate two kinds of the deepest cut generation problem, via sets or via functions. We then consider some special cases of the deepest cut generation problem which are amenable to ecient computation. We conclude with computational tests of one of these procedures on a large set of MIPLIB problems