Improved Convexity Cuts for Lattice Point Problems

The generalized lattice point (GLF) problem provides a formulation that accommodates a var.lety of discrete alternative problems. In this paper we show how to substantlrlly strengthen the convexity cuts for the GLF problem. The new cuts are based on the identification of "synthesized" lattice point conditions to replace those that ordinarily define the cut. The synthesized conditions give an alternative set of hyperplanes that enlarge the convex set, thus allowing the cut to be shifted deeper into the solution space. A convenient feature of the strengthened cuts is the existence of linking relationships by which they may be constructively generated from the original cuts. Geometrie examples are given in the last section to show how the new cuts improve upon those previously proposed for the GLF problem.