Everything about Global Optimum totally explained
In
mathematics, a
global optimum is a selection from a given domain which yields either the highest value or lowest value (depending on the objective), when a specific
function is applied. For example, for the function
» f(
x) = −
x2 + 2,
defined on the
real numbers, the global optimum occurs at
x = 0, when
f(
x) = 2. For all other values of
x,
f(
x) is smaller.
For purposes of
optimization, a function must be defined over the whole domain, and must have a range which is a
totally ordered set, in order that the evaluations of distinct domain elements are comparable.
By contrast, a
local optimum is a selection for which
neighboring selections yield values that are not greater. The concept of a
local optimum implies that the domain is a
metric space or
topological space, in order that the notion of "neighborhood" should be meaningful.
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