Intersection cuts - standard versus restricted

This note is meant to elucidate the difference between intersection cuts as originally defined, and intersection cuts as defined in the more recent literature. It also states a basic property of intersection cuts under their original definition. Intersection cuts for mixed integer programs were introduced in the early 1970’s [1, 2] as inequalities obtained by intersecting the extreme rays of the polyhedral cone C(B), where B is a basis of the linear programming relaxation P , with the boundary of some convex set T whose interior contains the vertex v(B) of P but no feasible integer point. Such a set T will be called PI-free, where PI is the set of feasible integer points. In particular, if the simplex tableau associated with the basis B is xB = x̄B − ∑