  We typically construct optimal designs based on a single objective function.
To better capture the breadth of an experiment's goals, we could instead
construct a multiple objective optimal design based on multiple objective
functions. While algorithms have been developed to find multi-objective optimal
designs (e.g. efficiency-constrained and maximin optimal designs), it is far
less clear how to verify the optimality of a solution obtained from an
algorithm. In this paper, we provide theoretical results characterizing
optimality for efficiency-constrained and maximin optimal designs on a discrete
design space. We demonstrate how to use our results in conjunction with linear
programming algorithms to verify optimality.
