An optimization problem can be represented in the following way: given a function $$f:A\to\mathbb{R}$$ from some set $$A$$ to the real numbers, we want to find 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").