Lagrangian

Assume that we have an optimization problem in the standard form: $$\text{minimize } f_0(x)$$ $$\begin{matrix}\text{subject to} & f_i(x) \le 0, \,\,\,\, i=1,\dots,m \\ & h_i(x) =0, \,\,\,\, i=1,\dots,p\end{matrix}$$