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A new approach to the construction of optimal designs. (English) Zbl 0799.62082
Summary: By combining a modified version of R. Hooke and T. A. Jeeves’ [J. Assoc. Comput. Mach. 8, 212-229 (1961; Zbl 0111.125)] pattern search with exact or Monte Carlo moment calculations, it is possible to find $$I$$-, $$D$$- and $$A$$-optimal (or nearly optimal) designs for a wide range of response-surface problems. The algorithm routinely handles problems involving the minimization of functions of 1000 variables, and so for example can construct designs for a full quadratic response-surface depending on 12 continuous process variables. The algorithm handles continuous or discrete variables, linear equality or inequality constraints, and a response surface that is any low degree polynomial. The design may be required to include a specified set of points, so a sequence of designs can be obtained, each optimal given that the earlier runs have been made. The modeling region need not coincide with the measurement region. The algorithm has been implemented in a program called “gosset”, which has been used to compute extensive tables of designs. Many of these are more efficient than the best designs previously known.

##### MSC:
 62K05 Optimal statistical designs 65C99 Probabilistic methods, stochastic differential equations 62-04 Software, source code, etc. for problems pertaining to statistics
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