Computing optimal experimental designs via interior point method

Zhaosong Lu, Ting Kei Pong

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17 Scopus citations


In this paper, we study optimal experimental design problems with a broad class of smooth convex optimality criteria, including the classical A-, D-, and 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 the Sherman-Morrison-Woodbury formula when the size of the moment matrix is small relative to the size of the design space. Finally, we compare our IP method with the widely used multiplicative algorithm introduced by [S. D. Silvey, D. M. Titterington, and B. Torsney, Commun. Statist. Theory Methods, 7 (1978), pp. 1379-1389] and the standard IP solver SDPT3 [K. C. Toh, M. J. Todd, and R. H. T̈uẗunc̈u, Optim. Methods Softw., 11/12 (1999), pp. 545-581], [R. H. T̈uẗunc̈u, K. C. Toh, and M. J. Todd, Math. Program. Ser. B, 95 (2003), pp. 189-217]. The computational results show that our IP method generally outperforms these two methods in both speed and solution quality.

Original languageEnglish (US)
Pages (from-to)1556-1580
Number of pages25
JournalSIAM Journal on Matrix Analysis and Applications
Issue number4
StatePublished - Dec 1 2013
Externally publishedYes


  • A-criterion
  • C-criterion
  • D-criterion
  • Interior point method
  • Optimal experimental design
  • Pth mean criterion


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