  We develop a new method for obtaining the BPS equations of static vortices
motivated by the results of the \textit{On-Shell} method on the standard
Maxwell-Higgs model and its Born-Infeld-Higgs model~\cite{Atmaja:2014fha}. Our
method relies on the existence of what we shall call an energy function, $Q$,
which is a mere function of the (effective) fields. The total energy of BPS
vortices, $E_{BPS}$, are simply given by a difference between the boundaries
value of $Q$ at $r\to\infty$ and at $r=0$, $E_{BPS}=Q(r\to\infty)-Q(r=0)$.
Imposing a condition that these (effective) fields are independent, we may
define a BPS Lagrangian, $\mathcal{L}_{BPS}$, derived by taking integral of
differential $Q$, $\mathcal{L}_{BPS}=-\int dQ$. Matching the Lagrangian
$\mathcal{L}_{BPS}$ with the corresponding effective Lagrangian, we can extract
several equations. Solving these equations yields the desired BPS equations
and, in some cases, also constraint equations. With our method, the various
known BPS equations of vortices are derived in a relatively simple procedure.
