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The problem of optimal experimental design for estimating parameters in linear regression models is placed in a general convex analysis setting. Duality results are obtained using two approaches, one based on subgradients and the other on Lagrangian theory. The subgradient concept is also used to derive a potentially useful equivalence theorm for establishing the optimality of a singular design and, finally, general versions of the original equivalence theorems of Kiefer and Wolfowitz (1960) are obtained.

Hern and Lawphongpanich (1987) studied the properties of the direction formed by taking the difference of two successive dual iterates of generalized linear programming (GLP), and pointed out that this direction is also solution to an associated direction finding problem. This study shows that this direction finding problem belongs to a new class of direction finding problems and propose a modification of GLP in which its original direction finding problems is replaced by another in this new class. This new direction finding problem is similar to the one used by Demyanov for minimax problems and guarantees an ascent direction for the dual function. Finally, we state and prove the convergence for the modified GLP. Supported in part by the Foundation Research Program of the Naval Postgraduate School with funds provided by the Chief of Naval Research and the National Science Foundation. http://archive.org/details/demyanovtypemodi00lawp N0001487WRE011 NA Approved for public release; distribution is unlimited.

We study monotone convex functions psi : L-0 (Omega, F, P) -> (-infinity, infinity] and derive a dual representation as well as conditions that ensure the existence of a sigma-additive subgradient. The results are motivated by applications in economic agents' choice theory.