A Comparison of Algorithms for Constructing Exact D-Optimal Designs

REFERENCES

• Atkinson , A. C. 1969 . Constrained maximization and the design of experiments . Technometrics , 11 : 616 – 618 .
   Web of Science ®Google Scholar
• Atwood , C. L. 1970 . Robust procedures for estimating polynomial regression School of Statistics, University of Minnesota. . Tech. Report No. 143
   Google Scholar
• Bloom , T. , Pfaffenberger , R. and Kochenberger , G. The efficient construction of optimal response surface designs based upon the |X'X| criterion . Presented at the 1972 American Statistical Association Meeting . August 14–18 , Montreal , Canada.
   Google Scholar
• Box , M. J. 1966 . A comparison of several current optimization methods, and the use of transformations in constrained problems . Computer J. , 9 : 67 – 77 .
   Web of Science ®Google Scholar
• Box , M. J. and Draper , N. R. 1971 . Factorial designs, the |X'X| criterion, and some related matters . Technometrics , 13 : 731 – 742 .
   Web of Science ®Google Scholar
• Crowder , H. , Dembo , R. S. and Mulvey , J. M. 1979 . On reporting computational experiments with mathematical software . ACM Trans. Math. Software , 5 ( 2 ) : 193 – 203 .
   Google Scholar
• Draper , N. R. and St. John , R. C. 1977 . A mixtures model with inverse terms . Technometrics , 19 : 37 – 46 .
   Web of Science ®Google Scholar
• Fedorov , V. V. 1969 . Theory of optimal experiments Moscow , USSR : Izd-vo Moscow State University. . Preprint No. 7 LSM
   Google Scholar
• Fedorov , V. V. 1972 . Theory of Optimal Experiments Edited by: Studden , W. J. and Klimko , E. M. New York : Academic Press. .
   Google Scholar
• Hartley , H. O. and Ruud , P. G. 1969 . “ Computer optimization of second order response surface designs. ” . In Statistical Computing Edited by: Milton , R. C. and Nelder , J. A. 441 – 462 . New York : Academic Press. .
   Google Scholar
• Kiefer , J. 1971 . “ The role of symmetry and approximation in exact design optimality. ” . In Statistical Decision Theory and Related Topics Edited by: Gupta , S. S. and Yachel , J. 109 – 118 . New York : Academic Press. .
   Google Scholar
• Mahoney , F. 1970 . The design of experiments for regression analysis by computer search procedures , Ph.D. thesis Operations Research and Statistics, Rensselaer Polytechnic Institute. .
   Google Scholar
• Mitchell , T. J. 1974 . An algorithm for the construction of D-optimal experimental designs . Technometrics , 16 : 203 – 211 .
   Web of Science ®Google Scholar
• Mitchell , T. J. and Miller , F. L. Jr. 1970 . Use of design repair to construct designs for special linear models 130 – 131 . Oak Ridge , TN : Oak Ridge National Laboratory. . Math. Div. Ann. Progr. Rept. (ORNL-4661)
   Google Scholar
• Nachtsheim , C. J. 1979 . Contributions to optimal experimental design , Ph.D. thesis Department of Applied Statistics, University of Minnesota. .
   Google Scholar
• Neuhardt , J. B. and Bradley , H. E. 1971 . Selection of multi-factor experimental arrangements with resource constraints . J. Amer. Statist. Assoc. , 66 : 618 – 621 .
   Web of Science ®Google Scholar
• Powell , M. J. D. 1964 . An efficient method for finding the minimum of a function of several variables without calculating derivatives . Computer J. , 7 : 155 – 162 .
   Web of Science ®Google Scholar
• St. John , R. C. 1973 . Models and designs for experiments with mixtures , Ph.D. thesis Department of Statistics, University of Wisconsin–Madison. .
   Google Scholar
• St. John , R. C. and Draper , N. R. 1975 . D-optimality for regression designs: A review . Technometrics , 17 : 15 – 22 .
   Web of Science ®Google Scholar
• St. John , R. C. and Draper , N. R. 1977 . Designs in three and four components and mixture models with inverse terms . Technometrics , 19 : 117 – 130 .
   Web of Science ®Google Scholar
• Van Schalkwyk , D. J. 1971 . On the design of mixture experiments , Ph.D. thesis University of London. .
   Google Scholar
• Wynn , H. P. 1972 . Results in the theory and construction of D-optimum experimental designs . J. Roy. Statis. Soc , B-34 : 133 – 147 .
   Google Scholar