A geometric interpretation of optimal design problems is given. This provides a unified treatment of the equivalence theorems for D-optimal and Ds-optimal designs in the form of duality theorems established by means of Strong Lagrangian Theory. The appropriate theorem for Ds-optimality is proved. A monotonic procedure for constructing D-optimal designs is suggested by the duality. This is described and its convergence established.
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Silvey et al. (1973) studied this question.
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