|Suppose that the response function f depends on a parameter x as shown at the right, and that x usually varies in the interval [A, B]|
|To model this process, we normally use the linearized model:
f 1 = a x with the adequate results.
|We maximize the response f 1(x), where x as a control. The optimization pushes x out of its original range. The linear model predicts the unlimited increase of x and of the response f 1(x).|
|It would be a mistake to keep the linear model, artificially restricting
the range of parameter (forbidding x to exceed an unjustified value
The result f_c would be far from the
real optimum f_opt.
Instead, one should improve the model.