We construct a relativistic ${}^{3}{P}_{0}$ wave function for scalar mesons within the framework of the light-front quark model (LFQM). This scalar wave function is used to perform relativistic calculations of absolute widths for the radiative decay processes ${(0}^{++})\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma},$ ${(0}^{++})\ensuremath{\rightarrow}\ensuremath{\varphi}\ensuremath{\gamma},$ and ${(0}^{++})\ensuremath{\rightarrow}\ensuremath{\rho}\ensuremath{\gamma}$ which incorporate the effects of glueball-$q\overline{q}$ mixing. The mixed physical states are assumed to be ${f}_{0}(1370),$ ${f}_{0}(1500),$ and ${f}_{0}(1710)$ for which the flavor-glue content is taken from the mixing calculations of other works. Since experimental data for these processes are poor, our results are compared with those of a recent non-relativistic model calculation. We find that while the relativistic corrections introduced by the LFQM reduce the magnitudes of the decay widths by 50\char21{}70 %, the relative strengths between different decay processes are fairly well preserved. We also calculate decay widths for the processes $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\varphi}}{(0}^{++})\ensuremath{\gamma}$ and ${(0}^{++})\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ involving the light scalars ${f}_{0}(980)$ and ${a}_{0}(980)$ to test the simple $q\overline{q}$ model of these mesons. Our results of the $q\overline{q}$ model for these processes are not consistent with well-established data, further supporting the idea that ${f}_{0}(980)$ and ${a}_{0}(980)$ are not conventional $q\overline{q}$ states.