A Nonlinear Programming Solution to the Dual Response Problem

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Abstract
Recently, Vining and Myers presented a methodology for achieving some of the goals of the Taguchi philosophy using response surface methods and a dual response optimization approach. This paper shows how the same goals can be achieved using standard nonlinear programming techniques, specifically, the generalized reduced gradient (GRG) algorithm. The procedure is illustrated using examples taken from the literature. It is shown that the proposed method can be more flexible and easier to use than the dual response approach and, in some cases, can give better solutions within the region of interest. In conclusion, it is shown how the method can be applied to multiple response mixture experiments.

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