  We present two alternative methods for optimizing minimum energy conical
intersection (MECI) molecular geometries without knowledge of the derivative
coupling (DC). These methods are based on the utilization of Lagrange
multipliers: i) one method uses an approximate calculation of the DC, while the
other ii) do not require the DC. Both methods use the fact that information of
the DC is contained in the Hessian of the squared energy difference. Tests done
on a set of small molecular systems, in comparison with other methods, show the
ability of the proposed methods to optimize MECIs. Finally, we apply the
methods to the furimamide molecule, to optimize and characterize its S$_1$
/S$_2$ MECI, and to optimizing the S$_0$ /S$_1$ MECI of the silver trimer.
