A graphical approach for the construction of constrained a and l-optimal designs using efficiency plots

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Abstract
In this paper, a graphical approach for computing constrained optimal designs in regression experiments is presented. The method is simple to implement and can be used in design problems where there are two optimality criteria, and these criteria are expressible as convex functionals of information matrices. The method is applied to seek constrained L and D-optimal designs in quadratic and cubic polynomial models. Several interesting features are noted, including (i) ifξ0 and ξ1 are optimal designs for two optimality criteria φ0 and φ1 and the two designs have the same support, the optimal design for a convex combination of φ0 and φ1 can have a different set of support points, and (ii) D-restricted extrapolation designs. are generally more efficient than A-restricted extrapolation designs for estimating the model parameters.

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