  We present the results of a statistical study of the star formation rates
(SFR) derived from the Galaxy Evolution Explorer (GALEX) observations in the
ultraviolet continuum and in the H\alpha emission line for a sample of about
800 luminous compact galaxies (LCGs). Galaxies in this sample have a compact
structure and include one or several regions of active star formation. Global
galaxy characteristics (metallicity, luminosity, stellar mass) are intermediate
between ones of the nearby blue compact dwarf (BCD) galaxies and Lyman-break
galaxies (LBGs) at high redshifts z > 2 - 3. SFRs were corrected for
interstellar extinction which was derived from the optical Sloan Digital Sky
Survey (SDSS) spectra. We find that SFRs derived from the galaxy luminosities
in the far ultraviolet (FUV) and near ultraviolet (NUV) ranges vary in a wide
range from 0.18 M_Sun/yr to 113 M_Sun/yr with median values of 3.8 M_Sun/yr and
5.2 M_Sun/yr, respectively. Simple regression relations are found for
luminosities L(H\alpha) and L(UV) as functions of the mass of the young stellar
population, the starburst age, and the galaxy metallicity. We consider the
evolution of L(H\alpha), L(FUV) and L(NUV) with a starburst age and introduce
new characteristics of star formation, namely the initial H\alpha, FUV and NUV
luminosities at zero starburst age.
