  We employ UV and optical photometry, from the GALEX and SDSS surveys
respectively, to study the star formation histories of 561 luminous infrared
galaxies (LIRGs) in the nearby Universe. A small fraction (~4%) of these
galaxies have spheroidal or near-spheroidal morphologies and could be
progenitors of elliptical galaxies. The remaining galaxies are morphologically
late-type or ongoing mergers. 61% of the LIRGs do not show signs of
interactions, while the remaining objects are either interacting (~18%) or show
post-merger morphologies (~19%). The (SSP-weighted) average age of the
underlying stellar populations in these objects is typically 5-9 Gyrs, with a
mean value of ~6.8 Gyrs. ~60% of the LIRG population began their recent star
formation (RSF) episode within the last Gyr, while the remaining objects began
their RSF episodes 1 to 3 Gyrs in the past. Up to 35% of the stellar mass in
the remnant forms in these episodes - the mean value is ~15%. The (decay)
timescales of the star formation are typically a few Gyrs, indicating that the
star formation rate does not decline significantly during the course of the
burst. 14% of the LIRG population host (Type 2) AGN. The AGN hosts exhibit UV
and optical colours that are redder than those of the normal (non-AGN)
population. However, there is no evidence for a systematically higher dust
content in the AGN hosts. AGN typically appear ~0.5-0.7 Gyrs after the onset of
star formation and the redder colours are a result of older RSF episodes, with
no measurable evidence of negative feedback from the AGN on the star formation
in their host galaxies. (abridged)
