Department researchers in the theory of optimal experimental design have developed theoretical optimal exact designs according to any one of several different optimality criteria (e.g., D-. A-, E- or G-optimality) accompanied by algorithms for finding these optimal designs for a wide variety of treatment structures and different design sizes (exact optimal designs). Algorithms have then been implemented numerically, often requiring iterative methods to be constructed that converged to the optimal solution. Department researchers in this field have solved optimal design problems in the context of fractional factorial experiments, comparisons of test treatments with a control, and linear and quadratic regression in both the classic cases of independent additive errors and with certain specialized correlated error structures for which a non-sequential solution was available.
Further research has involved development of approximate optimal designs where the design size is neither fixed nor (possibly) finite. This approach has led to sequential optimal design methodology and numerical applications, especially in the correlated error settings with regression model structure rather than a treatment structure. In addition, department researchers work with collaborators in various fields to develop appropriate designs for complex studies.