The discussion here is posed in terms of searching for a minimum (searching for a maximum is similar) of a unimodal function Unlike finding a zero, where two function evaluations with opposite sign are sufficient to bracket a root, when searching for a minimum, three values are necessary Arg max as an example, both unnormalised and normalised sinc functions above have of {0} because both attain their global maximum value of 1 at x = 0 The unnormalised sinc function (red) has arg min of {−4.49, 4.49}, approximately, because it has 2 global minimum values of approximately −0.217 at x = ±4.49. The value of the function at a maximum point is called the maximum value of the function, denoted , and the value of the function at a minimum point is called the minimum value of the function, (denoted for clarity). It represents a wide dynamic range of numeric values by using a floating radix point
The global optimum can be found by comparing the values of the original objective function at the points satisfying the necessary and locally sufficient conditions The method of lagrange multipliers relies on the intuition that at a maximum, f(x, y) cannot be increasing in the direction of any such neighboring point that also has g = 0. This is wrapping in contrast to saturating It is therefore the maximum value for variables declared as integers (e.g., as int) in many programming languages.
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