A geometric approach to optimal design theory

Abstract

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.