Optimization (mathematics)

In mathematics, the term optimization refers to study of problems in which one seeks for a minimum or a maximum of a real function within a given allowed set. This problem can be presented in the following way:

Given: a function f : A $\to$ R from some set A to the real numbers

Find: an element x₀ in A such that f(x₀) ≤ f(x) for all x in A ("minimization") or such that f(x₀) ≥ f(x) for all x in A ("maximization").