Removing non-optimal support points in D-optimum design algorithms

We show that points can be removed from the design space during the search for a D-optimum design, using a simple inequality satisfied by support points of a D-optimum design measure. This inequality does not seem to have been noticed before but may be used for accelerating algorithms for D-optimum design, or for the determination of minimum covering ellipsoids, as used, e.g., in ellipsoidal trimming.