Let's now consider as a second example, a general cutting plane method for mixed 0-1 integer linear programming based on a convexification approach. This method derives from a more general theoretical framework developed by Balas and others authors and has connections with both disjuntive programming and lift and project methods.
In a mixed 0-1 linear problem besides the usual linear constraints we impose the condition that some of the variables, let's say the first p, have to assume values in the set 0, 1. In the following K will stand for the feasible set of the linear relaxation, S will stand for the set of the feasible solutions of the mixed problem and P(S) for the closure of the convex hull of S.