On two problems over polyhedral convex sets

In this paper, we are concerned with the following two problems often encountered in concave programming: Given the vertices and extreme detections of a polyhedral convex set Modefined by a system of linear constraints, determine the vertices and extreme directions of the polyhedral convex set obtained from M just by adding one new linear equality (or inequality) constraint.Among the constraints of a given polyhedral convex set, find those which are redundant, i.e. which can be removed without affecting the polyhedral convex set.