  We present and discuss optical measurements of the faint end of the galaxy
luminosity function down to M_R = -10 in five different local environments of
varying galaxy density and morphological content. The environments we studied,
in order of decreasing galaxy density, are the Virgo Cluster, the NGC 1407
Group, the Coma I Group, the Leo Group and the NGC 1023 Group. Our results come
from a deep wide-angle survey with the NAOJ Subaru 8 m Telescope on Mauna Kea
and are sensitive down to very faint surface-brightness levels. Galaxies were
identified as group or cluster members on the basis of their surface brightness
and morphology. The faintest galaxies in our sample have R ~ 22.5. There were
thousands of fainter galaxies but we cannot distinguish cluster members from
background galaxies at these faint limits so do not attempt to determine a
luminosity function fainter than M_R = -10.
  In all cases, there are far fewer dwarfs than the numbers of low mass halos
anticipated by cold dark matter theory. The mean logarithmic slope of the
luminosity function between M_R = -18 and M_R = -10 is alpha ~ -1.2, far
shallower than the cold dark matter mass function slope of alpha ~ -1.8. We
would therefore need to be missing about 90 per cent of the dwarfs at the faint
end of our sample in all the environments we study to achieve consistency with
CDM theory.
