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Biometrika 1973 60(1):21-32; doi:10.1093/biomet/60.1.21
© 1973 by Biometrika Trust
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A geometric approach to optimal design theory

S. D. SILVEY and D. M. TITTERINGTON

University of Glasgow

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.

Key Words: D-optimality • Ds-optimality • Strong Lagrangian duality theory • Design construction • Game theory


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