16Surface Analysis II
16.1 Introduction
Modifying objective functions, in general, does not make the optimization solution faster, but it can have advantages in visualizing the surface, in seeing issues, in scaling it for presentation, or in simplifying a calculation. If you modify the OF, however, you need to ensure that your modification does not change the DV* solution.
Modifying the objective function is often useful for simplifying the optimization exercise. For example,
finds the same model coefficients as
And
finds the same θ value as
Here are proofs for various OF transformations.
16.2 Maximize Is Equivalent to Minimize the Negative
Proof: Consider that 
and that a maximum exists at x* with an OF* value and then 
for any
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