  We present optical follow-up imaging obtained with the Katzman Automatic
Imaging Telescope, Las Cumbres Observatory Global Telescope Network, Nickel
Telescope, Swope Telescope, and Thacher Telescope of the LIGO/Virgo
gravitational wave (GW) signal from the neutron star-black hole (NSBH) merger
GW190814. We searched the GW190814 localization region (19 deg$^{2}$ for the
90th percentile best localization), covering a total of 51 deg$^{2}$ and 94.6%
of the two-dimensional localization region. Analyzing the properties of 189
transients that we consider as candidate counterparts to the NSBH merger,
including their localizations, discovery times from merger, optical spectra,
likely host-galaxy redshifts, and photometric evolution, we conclude that none
of these objects are likely to be associated with GW190814. Based on this
finding, we consider the likely optical properties of an electromagnetic
counterpart to GW190814, including possible kilonovae and short gamma-ray burst
afterglows. Using the joint limits from our follow-up imaging, we conclude that
a counterpart with an $r$-band decline rate of 0.68 mag day$^{-1}$, similar to
the kilonova AT 2017gfo, could peak at an absolute magnitude of at most $-17.8$
mag (50% confidence). Our data are not constraining for ''red'' kilonovae and
rule out ''blue'' kilonovae with $M>0.5 M_{\odot}$ (30% confidence). We
strongly rule out all known types of short gamma-ray burst afterglows with
viewing angles $<$17$^{\circ}$ assuming an initial jet opening angle of
$\sim$$5.2^{\circ}$ and explosion energies and circumburst densities similar to
afterglows explored in the literature. Finally, we explore the possibility that
GW190814 merged in the disk of an active galactic nucleus, of which we find
four in the localization region, but we do not find any candidate counterparts
among these sources.
