  We consider the orbital evolution of the S-stars, the young main-sequence
stars near the supermassive black hole (SBH) at the Galactic center (GC), and
put constraints on competing models for their origin. Our analysis includes for
the first time the joint effects of Newtonian and relativistic perturbations to
the motion, including the dragging of inertial frames by a spinning SBH as well
as torques due to finite-N asymmetries in the field-star distribution (resonant
relaxation, RR). The evolution of the S-star orbits is strongly influenced by
the Schwarzschild barrier (SB), the locus in the (E,L) plane where RR is
ineffective at driving orbits to higher eccentricities. Formation models that
invoke tidal disruption of binary stars by the SBH tend to place stars below
(i.e., at higher eccentricities than) the SB; some stars remain below the
barrier, but most stars are able to penetrate it, after which they are subject
to RR and achieve a nearly thermal distribution of eccentricities. This process
requires roughly 50 Myr in nuclear models with relaxed stellar cusps, or >~10
Myr, regardless of the initial distribution of eccentricities, in nuclear
models that include a dense cluster of 10 M_Sun black holes. We find a
probability of <~1% for any S-star to be tidally disrupted by the SBH over its
lifetime.
