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.
"General Differential and Lagrangian Theory for Optimal Experimental Design." Ann. Statist. 11 (4) 1060 - 1068, December, 1983. https://doi.org/10.1214/aos/1176346321