Computing c-optimal experimental designs using the simplex method of linear programming

An experimental design is said to be c-optimal if it minimizes the variance of the best linear unbiased estimator of cTβ , where c is a given vector of coefficients, and β is an unknown vector parameter of the model in consideration. For a linear regression model with uncorrelated observations and a finite experimental domain, the problem of approximate c-optimality is equivalent to a specific linear programmingproblem. Themost important consequence of the linear programming characterization is that it is possible to base the calculation of c-optimal designs on well-understood computational methods. In particular, the simplex algorithm of linear programming applied to the problem of c-optimality reduces to an exchange algorithm with different pivot rules corresponding to specific techniques of selecting design points for exchange. The algorithm can also be applied to ‘‘difficult’’ problems with singular c-optimal designs and relatively high dimension of β . Moreover, the algorithm facilitates identification of the set of all the points that can support some c-optimal design. As an example, optimal designs for estimating the individual parameters of the trigonometric regression on a partial circle are computed. © 2008 Elsevier B.V. All rights reserved.