Abstract: 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. However, although algorithms have been developed to find such designs (e.g., efficiency-constrained and maximin optimal designs), it is far less clear how to verify the optimality of a solution obtained from these algorithms. In this paper, we provide theoretical results that characterize optimality for efficiency-constrained and maximin optimal designs on a discrete design space. Lastly, we demonstrate how to use our results with linear programming algorithms to verify optimality.

Key words and phrases: Convex optimization, efficiency, linear programming, maximin design, optimality conditions, robustness.