Consider the following claim: - Suppose you have two
*distinct*valid inequalities \(ax \le b\) and \(cx \le d\). Further suppose that your polyhedron is*full-dimensional*. Then the aggregated inequality \( (a+c)x \le (b+d) \) cannot induce a facet.
This claim is true, and I have used it in my research. However, I was hoping to find it explicitly stated in literature. Other researchers have referred me to Schrijver's Theory of LP and IP, but I cannot seem to find it. (Perhaps it is too trivial a result to include.) Is this claim made in any published material?
asked
Austin Buchanan |

It seems to me that this is an easy consequence of the fact that the set of facets forms a minimal description of the polyhedron, so removing one must produce a strictly larger polyhedron. That can't be true of an aggregated inequality if the component inequalities are part of the description.
answered
Matthew Salt... ♦ |