The Optimization of Response Surface Designs

摘要

The report applies the techniques of non-convex non-linear programming to the problem of optimizing experimental designs in response surface analysis. Specifically, response surfaces which are quadratic or cubic in the input factors are considered. The region of experimentation is bounded by hyperplanes but specifically hypercubes are considered in the evaluation of optimum designs. The procedure employs the Rosen projected gradient method with a statistical sample of starting points. The objective function employed is the generalized variance of the estimated effect coefficients in the estimated response surface analysis. The report also contains a critical evaluation of this objective function and a comparison with the techniques by Box and Draper which has been successfully used in small scale problems. (Author)