Combinatorial behavior of extreme points of perturbed polyhedra

Abstract

Two polyhedral convex sets A and B are considered, where A and B have the same set of defining linear forms but differ in a least one right-hand-side resource. Upper bounds are established for the Euclidean distance between an extreme point of A and an extreme point of B, and then for the Hausdorff distance between sets A and B. Both bounds involve a scaler multiple of the Euclidean distance between the resource vectors. Combinatorial arguments are employed to establish the scalers. An application to stability theory for mathematical programming is given.