  The problem of computing an exact experimental design that is optimal for the
least-squares estimation of the parameters of a regression model is considered.
We show that this problem can be solved via mixed-integer linear programming
(MILP) for a wide class of optimality criteria, including the criteria of A-,
I-, G- and MV-optimality. This approach improves upon the current
state-of-the-art mathematical programming formulation, which uses mixed-integer
second-order cone programming. The key idea underlying the MILP formulation is
McCormick relaxation, which critically depends on finite interval bounds for
the elements of the covariance matrix of the least-squares estimator
corresponding to an optimal exact design. We provide both analytic and
algorithmic methods for constructing these bounds. We also demonstrate the
unique advantages of the MILP approach, such as the possibility of
incorporating multiple design constraints into the optimization problem,
including constraints on the variances and covariances of the least-squares
estimator.
