A-optimality ("average" or trace)
One criterion is A-optimality, which seeks to minimize the trace of the inverse of the information matrix. This criterion results in minimizing the average variance of the estimates of the regression coefficients.
C-optimality
This criterion minimizes the variance of a best linear unbiased estimator of a predetermined linear combination of model parameters.
D-optimality (determinant)
A popular criterion is D-optimality, which seeks to minimize |(X'X)−1|, or equivalently maximize the determinant of the information matrix X'X of the design. This criterion results in maximizing the differential Shannon information content of the parameter estimates.
E-optimality (eigenvalue)
Another design is E-optimality, which maximizes the minimum eigenvalue of the information matrix.
T-optimality
This criterion maximizes the trace of the information matrix.
Other optimality-criteria are concerned with the variance of predictions:
G-optimality
A popular criterion is G-optimality, which seeks to minimize the maximum entry in the diagonal of the hat matrix X(X'X)−1X'. This has the effect of minimizing the maximum variance of the predicted values.
I-optimality (integrated)
A second criterion on prediction variance is I-optimality, which seeks to minimize the average prediction variance over the design space.
V-optimality (variance)
A third criterion on prediction variance is V-optimality, which seeks to minimize the average prediction variance over a set of m specific points.[9]