  We consider quantum electrodynamics quantized on the light front in Feynman
gauge and regulated in the ultraviolet by the inclusion of massive,
negative-metric Pauli--Villars (PV) particles in the Lagrangian. The eigenstate
of the electron is approximated by a Fock-state expansion truncated to include
one photon. The Fock-state wave functions are computed from the fundamental
Hamiltonian eigenvalue problem and used to calculate the anomalous magnetic
moment, as a point of comparison. Two approaches are considered: a
sector-dependent parameterization, where the bare parameters of the Lagrangian
are allowed to depend on the Fock sectors between which the particular
Hamiltonian term acts, and the standard choice, where the bare parameters are
the same for all sectors. Both methods are shown to require some care with
respect to ultraviolet divergences; neither method can allow all PV masses to
be taken to infinity. In addition, the sector-dependent approach suffers from
an infrared divergence that requires a nonzero photon mass; due to
complications associated with this divergence, the standard parameterization is
to be preferred. We also show that the self-energy effects obtained from a
two-photon truncation are enough to bring the standard-parameterization result
for the anomalous moment into agreement with experiment within numerical
errors. This continues the development of a method for the nonperturbative
solution of strongly coupled theories, in particular quantum chromodynamics.
