Approximate D-optimal designs of experiments on the convex hull of a finite number of information matrices

In the paper we solve the problem of DH-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite number of positive semidefinite matrices. The problem of DH-optimality covers many special design settings, e.g. the D-optimal experimental design for regression models with grouped observations. For DH-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that DH-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane.