Computing Optimal Experimental Designs via Interior Point Method

In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, Dand pth mean criterion. In particular, we propose an interior point (IP) method for them and establish its global convergence. Further, by exploiting the structure of the Hessian matrix of the optimality criteria, we derive an explicit formula for computing its rank. Using this result, we then demonstrate that the Newton direction arising in the IP method can be computed efficiently via Sherman-MorrisonWoodbury formula when the size of the moment matrix is small relative to the size of design space. Finally, we compare our IP method with the widely used multiplicative algorithm introduced by Silvey et al. [33] and the standard IP solver SDPT3 [36, 40]. The computational results show that our IP method generally outperforms these two methods in both speed and solution quality.