Response Surface Optimization When Experimental Factors Are Subject to Costs and Constraints

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Abstract
This paper deals with problems of response surface optimization in which the control variables and responses are subject to costs and constraints. Relationships between control variables and the cost or constraint functions are treated as additional response surfaces if explicit algebraic models are unavailable. Optimization methods are suggested which are based on gradient search and nonlinear programming techniques. To assure operating conditions within the specified constraint set a method based on feasible directions is used to control the search pattern. A scale-invariant gradient search method is suggested. Because it leads to an economical path to the maximum point the method has been dubbed “cheapest ascent.” The selection of measurement scales for the control variables is also discussed.

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