Convex optimization

A convex optimization problem (in standard form) can be written as : $$\text{minimize} f_0(x)$$ $$\begin{matrix}\text{subject to} & f_i(x) \le 0, \,\,\,\, i=1,\dots,m \\ & h_i(x) =0, \,\,\,\, i=1,\dots,p\end{matrix}$$