Optimal Designs Technique for Locating the Optimum of a Second Order Response Function

Abstract

A more efficient method of locating the optimum of a second order response function was of interest in this work. In order to do this, the principles of optimal designs of experiment is invoked and used for this purpose. At the end, it was discovered that the noticeable pitfall in response surface methodology (RSM) was circumvented by this method as the step length was obtained by taking the derivative of the response function rather than doing so by intuition or trial and error as is the case in RSM. A numerical illustration shows that this method is suitable for obtaining the desired optimizer in just one move which compares favourably with other known methods such as Newton-Raphson method which requires more than one iteration to reach the optimizer.

The Optimum of a Quadratic Univariate Response Function Is Located at the Origin

“…[1] and [2] stated that even though very few problems exist in real life where managers are concerned with taking decisions involving only one decision variable, this kind of study is justified since it forms the basis of simple extensions which plays a cardinal role to the development of a general multivariate algorithm (see [3]). …”