Application of semi-definite programming to the design of multi-response experiments

References

• Angelis , L. , Bora-Senta , E. and Moyssiadis , C. 2001 . Optimal exact experimental designs with correlated errors through a simulated annealing algorithm . Computational Statistics & Data Analysis , 37 : 275 – 296 .
   Web of Science ®Google Scholar
• Löfberg . 2005 . YALMIP . Available at http://control.ee.ethz.ch/∼joloef/yalmip.php. Version 3
   Google Scholar
• Atkinson , A. C. and Donev , A. N. 1992 . Optimum Experimental Designs , Oxford , , UK : Oxford University Press .
   Google Scholar
• Bischoff , W. 1993 . On D-optimal designs for linear models under correlated observations with an application to a linear model with multiple response . Journal of Statistical Planning and Inference , 37 : 69 – 80 .
   Web of Science ®Google Scholar
• Borkowski , J. J. 2003 . Using a genetic algorithm to generating small exact response surface designs . Journal of Probability and Statistical Science , 1 ( 1 ) : 65 – 88 .
   Google Scholar
• Boyd , S. and Vandenberghe , L. 2004 . Convex Optimization , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• Chang , S. I. 1994 . Some properties of multi-response D-optimal designs . Journal of Mathematical Analysis and Applications , 184 : 256 – 262 .
   Web of Science ®Google Scholar
• Chang , S. I. 1997 . An algorithm to generate near D-optimal designs for multiple-response surface models . IIE Transactions , 29 : 1073 – 1081 .
   Web of Science ®Google Scholar
• Chang , F. , Huang , M. L. , Lin , D. K.J. and Yang , H. 2001 . Optimal designs for dual response polynomial regression models . Journal of Statistical Planning and Inference , 93 : 309 – 322 .
   Web of Science ®Google Scholar
• Cook , R. D. and Nachtsheim , C. H. 1980 . A comparison of algorithms for constructing exact D-optimal designs . Technometrics , 22 ( 3 ) : 315 – 324 .
   Web of Science ®Google Scholar
• Drain , D. , Carlyle , W. M. , Montogomery , D. C. , Borror , C. and Cook , C. A. 2004 . A genetic algorithm hybrid for constructing optimal response surface designs . Quality and Reliability Engineering International , 20 ( 7 ) : 637 – 650 .
   Web of Science ®Google Scholar
• Draper , N. R. and Hunter , W. G. 1966 . Design of experiments for parameter estimation in multiresponse situations . Biometrika , 53 : 525 – 533 .
   Web of Science ®Google Scholar
• Fedorov , V. V. 1972 . Theory of Optimal Experiments , New York , NY : Academic Press .
   Google Scholar
• Gaffke , N. and Heiligers , B. 1995 . Algorithms for optimal design with application to multiple polynomial regressions . Metrika , 42 : 173 – 190 .
   Google Scholar
• Heredia-Langner , A. , Montgomery , D. C. , Carlyle , W. M. and Borror , C. 2004 . Model-robust optimal designs: a genetic algorithm approach . Journal of Quality Technology , 36 ( 3 ) : 263 – 279 .
   Web of Science ®Google Scholar
• Holmstrom , K. 2004 . TOMLAB Version 4.4 , San Diego , CA : Tomlab Optimization Inc. .
   Google Scholar
• Imhof , L. 2000 . Optimum designs for a multi-response regression model . Journal of Multivariate Analysis , 72 : 120 – 131 .
   Web of Science ®Google Scholar
• Jung , J. S. and Yum , B. J. 1996 . Construction of exact D-optimal designs by tabu search . Computational Statistics & Data Analysis , 21 : 181 – 191 .
   Web of Science ®Google Scholar
• Khuri , A. I. and Cornell , J. A. 1996 . Response Surfaces: Designs and Analyses, , 2nd edn. , New York , NY : Marcel Dekker .
   Google Scholar
• Krafft , O. and Schaefer , M. 1992 . D-optimal designs for a multivariate regression model . Journal of Multivariate Analysis , 42 : 130 – 140 .
   Web of Science ®Google Scholar
• Lewis , A. S. and Overton , M. L. 1996 . Eigenvalue optimization . Acta Numerica , 5 : 149 – 190 .
   Google Scholar
• Pukelsheim , F. 1993 . Optimal Design of Experiments , New York , NY : Wiley .
   Google Scholar
• Roy , S. N. , Gnanadesikan , R. and Srivastava , J. N. 1971 . Analysis and Design of Certain Quantitative Multiresponse Experiments , New York , NY : Pergamon Press .
   Google Scholar
• Shah , H. K. , Montgomery , D. C. and Carlyle , W. M. 2004 . Response surface modeling and optimization in multi-response experiments using seemingly unrelated regression . Quality Engineering , 16 ( 3 ) : 387 – 397 .
   Google Scholar
• Todd , M. J. 2001 . Semidefinite optimization . Acta Numerica , 10 : 515 – 560 .
   Google Scholar
• Vandenberghe , L. and Boyd , S. 1996 . Semidefinite programming . SIAM Review , 38 ( 1 ) : 49 – 95 .
   Web of Science ®Google Scholar
• Wijesinha , M. M.C. 1984 . Design of experiments for multiresponse models , Ph.D. thesis Gainesville , FL : Department of Statistics, University of Florida .
   Google Scholar
• Zellner , A. 1962 . An efficient method of estimating seeming unrelated regressions and tests for aggregation bias . American Statistical Association Journal , 57 : 348 – 368 .
   Web of Science ®Google Scholar