General differential and Lagrangian theory for optimal experimental design (Q1075728)

The paper provides a treatment of optimal experimental designs using the differential theory of convex analysis with the concept of the subgradient. Also included is a Lagrangian duality treatment. This paper is closely related to the first author's paper in J. Stat. Plann. Inference 4, 339-364 (1980; Zbl 0472.62079). The interest lies in estimating s linearly independent linear functions of the unknown parameters. The main result is the proof of a theorem on duality in terms of subgradients. This result is also proved applying to strong Lagrangian principle. For singular information matrices an optimality condition formulated by \textit{S. D. Silvey} [Biometrika 65, 553-559 (1978; Zbl 0391.62054)] is proved to be necessary. The equivalence result of \textit{J. Kiefer} and \textit{J. Wolfowitz} [Can. J. Math. 12, 363-366 (1960; Zbl 0093.156)] is extended to information functionals.