Basic exciton parameters, the energy of exciton transition and the radiative and nonradiative broadenings, are experimentally studied by means of reflectance spectroscopy for a heterostructure with the 14-nm GaAs/AlGaAs quantum well. Particular attention is paid to the nonradiative broadening which is sensitive to optical creation of free carriers and long-lived nonradiative excitons. A sublinear increase of the broadening of the heavy-hole and light-hole exciton resonances is observed when the light-hole exciton resonance is excited with increasing power. A simple model is developed, which allows one to well reproduce the observed dependence.