General form of an optimisation problem

Optimisation problems can be formulated in the following general form:

$$\min f(x)$$

$$x\in X$$ subject to

where $X\subset {\mathbb{R}}^n$ and $f(x)$ is a function ${\mathbb{R}}^n\rightarrow {\mathbb{R}}$. This means that the aim is to find x which belongs to a given domain X such that the objective function f is minimised. If a problem is a maximisation problem instead then one can turn it into the above form by using min -f(x) instead of max f(x).