Given: a function $f: A \to \mathbb{R}$ from some set $A$ to the real numbers. Sought: an element $x_0 \in A$ such that $f(x_0) \le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0) \ge f(x)$ for all $x \in A$ ("maximization).