  Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering
feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to form in
the radiative shock in the accretion column. High-luminosity NSs show a smooth
anti-correlation between the cyclotron-line centroid ($E_{CRSF}$) and X-ray
luminosity ($L_X$). The observed $E_{CRSF}-L_X$ smooth anti-correlation has
been in tension with the theoretically predicted one by the radiative shock
model. Since there is no other candidate site for the cyclotron-line formation,
we re-examine the predicted rate of change of the cyclotron-line energy with
luminosity at the radiative shock, taking a closer look at the Physics
involved. We developed a purely analytical model describing the overall
dependence of the observed cyclotron energy centroid on the shock front's
height, including the relativistic boosting effect due to the mildly
relativistic motion of the accreting plasma upstream with respect to the
shock's reference frame and the gravitational redshift. We find that the CRSF
energy varies with a) the shock height due to the dipolar magnetic field, b)
the Doppler boosting between the shock and bulk-motion frames, and c) the
gravitational redshift. We show that the relativistic effects noticeably weaken
the predicted $E_{CRSF}-L_X$ anti-correlation. We use our model to fit the data
of the X-ray source V0332+53 and demonstrate that the model fits the data
impressively well, alleviating the tension between observations and theory. The
reported $E_{CRSF}-L_X$ weak anti-correlation in the supercritical accretion
regime may be explained by the combination of the variation of the
magnetic-field strength along the accretion column, the effect of Doppler
boosting, and the gravitational redshift. Thus, the actual magnetic field on
the NS surface may be a factor of $\sim 2$ larger than the naively inferred
value from the observed CRSF.
