  We study the optimization of the Apodized Pupil Lyot Coronagraph (APLC) in
the context of exoplanet imaging with ground-based telescopes. The APLC
combines an apodization in the pupil plane with a small Lyot mask in the focal
plane of the instrument. It has been intensively studied in the literature from
a theoretical point of view, and prototypes are currently being manufactured
for several projects. This analysis is focused on the case of Extremely Large
Telescopes, but is also relevant for other telescope designs.
  We define a criterion to optimize the APLC with respect to telescope
characteristics like central obscuration, pupil shape, low order segment
aberrations and reflectivity as function of the APLC apodizer function and mask
diameter. Specifically, the method was applied to two possible designs of the
future European-Extremely Large Telescope (E-ELT).
  Optimum configurations of the APLC were derived for different telescope
characteristics. We show that the optimum configuration is a stronger function
of central obscuration size than of other telescope parameters. We also show
that APLC performance is quite insensitive to the central obscuration ratio
when the APLC is operated in its optimum configuration, and demonstrate that
APLC optimization based on throughput alone is not appropriate.
