  The high mass-loss rates of red supergiants (RSGs) drastically affect their
evolution and final fate, but their mass-loss mechanism remains poorly
understood. Various empirical prescriptions scaled with luminosity have been
derived in the literature, yielding results with a dispersion of 2-3 orders of
magnitude. We determine an accurate mass-loss rate relation with luminosity and
other parameters using a large, clean sample of RSGs and explain the
discrepancy between previous works. We assembled a sample of 2,219 RSG
candidates in the Large Magellanic Cloud, with ultraviolet to mid-infrared
photometry in up to 49 filters. We determined the luminosity of each RSG by
integrating the spectral energy distribution and the mass-loss rate using the
radiative transfer code DUSTY. Our derived RSG mass-loss rates range from
$10^{-9} M_\odot$ yr$^{-1}$ to $10^{-5} M_\odot$ yr$^{-1}$, mainly depending on
the luminosity. The average mass-loss rate is $9.3\times 10^{-7} M_\odot$
yr$^{-1}$ for $\log{(L/L_\odot)}>4$. We established a mass-loss rate relation
as a function of luminosity and effective temperature. Furthermore, we found a
turning point in the relation of mass-loss rate versus luminosity relation at
approximately $\log{(L/L_\odot)} = 4.4$, indicating enhanced rates beyond this
limit. We show that this enhancement correlates with photometric variability.
Moreover, we compared our results with prescriptions from the literature,
finding an agreement with works assuming steady-state winds. Additionally, we
examined the effect of different assumptions on our models and found that
radiatively driven winds result in mass-loss rates higher by 2-3 orders of
magnitude, which are unrealistically high for RSGs. Finally, we found that 21%
of our sample constitute current binary candidates. This has a minor effect on
our mass-loss relation.
