In this paper we study interior point (IP) methods for solving optimal design problems. In particular, we propose a primal IP method for solving the problems with general convex optimality criteria and establish its global convergence. In addition, we reformulate the problems with A-, D- and E-criterion into linear or log-determinant semidefinite programs (SDPs) and apply standard primal-dual IP solvers such as SDPT3 [21,25] to solve the resulting SDPs. We also compare the IP methods with the widely used multiplicative algorithm introduced by Silvey et al. . The computational results show that the IP methods generally outperform the multiplicative algorithm both in speed and solution quality. Moreover, our primal IP method theoretically converges for general convex optimal design problems while the multiplicative algorithm is only known to converge under some assumptions.
Manuscript, Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada, September 2010