  We investigate the dynamics of vortices in repulsive Bose-Einstein
condensates in the presence of an optical lattice (OL) and a parabolic magnetic
trap. The dynamics is sensitive to the phase of the OL potential relative to
the magnetic trap, and depends less on the OL strength. For the cosinusoidal OL
potential, a local minimum is generated at the trap's center, creating a stable
equilibrium for the vortex, while in the case of the sinusoidal potential, the
vortex is expelled from the center, demonstrating spiral motion. Cases where
the vortex is created far from the trap's center are also studied, revealing
slow outward-spiraling drift. Numerical results are explained in an analytical
form by means of a variational approximation. Finally, motivated by a discrete
model (which is tantamount to the case of the strong OL lattice), we present a
novel type of vortex consisting of two pairs of anti-phase solitons.
