# Optimization (mathematics)

From Citizendium, the Citizens' Compendium

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***R**from some set*A*to the real numbers*Find:*an element*x*_{0}in*A*such that*f*(*x*_{0}) ≤*f*(*x*) for all*x*in*A*(*minimization*) or such that*f*(*x*_{0}) ≥*f*(*x*) for all*x*in*A*(*maximization*).