A branch-and-bound algorithm for the exact optimal experimental design problem

We discuss a generalisation of the approximate optimal experimental design problem, in which the weight of each regression point needs to stay in a closed interval. We work with Kiefer’s optimality criteria which include the well-known D- and A-optimality as special cases. We propose a first-order algorithm for the generalised problem that redistributes the weights of two regression points in each iteration. We develop a branch-and-bound algorithm for exact optimal experimental design problems under Kiefer’s criteria where the subproblems in the search tree are equivalent to the generalized approximate design problem, and therefore, can be solved efficiently by the first-order method. We observe that our branch-and-bound algorithm is favourable to a popular exchange heuristic for certain problem instances.